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Almost everywhere

In measure theory, a property holds everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities. The notion of "almost everywhere" is a companion notion to the concept of measure zero, is analogous to the notion of "almost surely" in probability—a field, based on measure theory. More a property holds everywhere if it holds for all elements in a set except a subset of measure zero, or equivalently, if the set of elements for which the property holds is conull. In cases where the measure is not complete, it is sufficient that the set be contained within a set of measure zero; when discussing sets of real numbers, the Lebesgue measure is assumed unless otherwise stated. The term everywhere is abbreviated a.e.. A set with full measure is one. In probability theory, the terms surely certain and always refer to events with probability 1 not including all of the outcomes; these are the sets of full measure in a probability space. Instead of saying that a property holds everywhere, it is said that the property holds for all elements.

If is a measure space, a property P is said to hold everywhere in X if there exists a set N ∈ Σ with μ = 0, all x ∈ X ∖ N have the property P. Another common way of expressing the same thing is to say that "almost every point satisfies P ", or that "for every x, P holds", it is not required that the set has measure 0. By the above definition, it is sufficient that be contained in some set N, measurable and has measure 0. If property P holds everywhere and implies property Q property Q holds everywhere; this follows from the monotonicity of measures. If is a finite or a countable sequence of properties, each of which holds everywhere their conjunction ∀ n P n holds everywhere; this follows from the countable sub-additivity of measures. By contrast, if x ∈ R is an uncountable family of properties, each of which holds everywhere their conjunction ∀ x P x does not hold everywhere. For example, if μ is Lebesgue measure on X = R and P x is the property of not being equal to x each P x holds everywhere, but the conjunction ∀ x P x does not hold anywhere.

As a consequence of the first two properties, it is possible to reason about "almost every point" of a measure space as though it were an ordinary point rather than an abstraction. This is done implicitly in informal mathematical arguments. However, one must be careful with this mode of reasoning because of the third bullet above: universal quantification over uncountable families of statements is valid for ordinary points but not for "almost every point". Outside of the context of real analysis, the notion of a property true everywhere is sometimes defined in terms of an ultrafilter. An ultrafilter on a set X is a maximal collection F of subsets of X such that: If U ∈ F and U ⊆ V V ∈ F The intersection of any two sets in F is in F The empty set is not in FA property P of points in X holds everywhere, relative to an ultrafilter F, if the set of points for which P holds is in F. For example, one construction of the hyperreal number system defines a hyperreal number as an equivalence class of sequences that are equal everywhere as defined by an ultrafilter.

The definition of everywhere in terms of ultrafilters is related to the definition in terms of measures, because each ultrafilter defines a finitely-additive measure taking only the values 0 and 1, where a set has measure 1 if and only if it is included in the ultrafilter. Dirichlet's fun

Unos Pocos con Valor

Unos Pocos con Valor is a Honduran film based on the book Los Pájaros de Belén by Mario Berrios, released in Honduras on August 20th 2010. Based on real life events, the story follows a group of special forces police officers who come up against the most dangerous gang in Honduras. Directed by Costa Rican Douglas Martin, the film's executive producers were Ismael Bevilacqua and Marisol Santos alongside Associate Producer Kattia Dominguez. Sixteen foreigners were in charge of camera direction and special effects and it was shot on location in San Pedro Sula, Siguatepeque, La Lima and El Progreso, Yoro. Post-production took place in Costa Rica, on the now closed post company called Dart, everything was done on Final Cut Pro and Later moved to an Avid DS for its mastering; the post, including finishing the edit, color correction, sound design and mastering was done in a period of 5 days by a small post team. The main Honduran cast consisted of 13 policemen, 13 criminals and eight women representing the wives of criminals, victims of abduction and secretaries, along with 21 supporting actors and four extras.

Alvaro Matute as Mauricio Barrientos - Pajaro 10 – Honduran Police Captain. Oscar Izaguirre as Moises Bustamante – A delinquent. Juan Funes as Pájaro 70 – Honduran Police. Angel Funes as Chekko – Young Delinquent. Juan Funes Padre as Andres – Abducted son's father. Jenifer Sosa as Nadia Dipalma – Abductee Anuar Vindel as Agent – from San Pedro Sula. Jose Moncada as Eleazar Torres – Specialist 1. Jakeline Salgado as Marcia Sosa De Uribe. Jorge Colindres as Chele Dinamita – A delinquent. Jose Barrientos as Rodriguez – Deputy Commissioner. Mauricio Alberto Sanchez Velez – A delinquent. Thania Zabala as Maria Isabel Maurtua Dayani. Javier Mugartegui as Saul Lozano – A lame man. Victor Fajardo as Salomon Bustamante – A delinquent. Xiomara Mejia as Yolanda Paz – Yoli. Henry Quiroz as Ramos – Pajaro 20. Federico Valdez as Francisco Caceres – Don Lente Andrea Reyes as Paola Robleda – Daughter. Daniel Fernandez as Abraham Bastamente – A delinquent. Carmen Pineda as pregnant woman – Victim in the opening scene. Http:// Official website

Associação de Escuteiros de Angola

The Associação de Escuteiros de Angola, the national Scouting organization of Angola, was founded in 1994 and became a member of the World Organization of the Scout Movement on June 13, 1998, was welcomed into WOSM at the World Scout Conference in South Africa in July 1999. The association is a member of the Comunidade do Escutismo Lusófono; the coeducational Associação de Escuteiros de Angola has 13,777 members as of 2008, in 54 groups spread over the country. Angola is the newest member of the Southern Zone of the Africa Region. Although Scouting is growing, the country is plagued by years of civil war and political unrest, this is hindering development in rural areas. Angolan Scouting was widespread in the colonial years, working with Portugal's Catholic Corpo Nacional de Escutas; when Angola gained its independence in 1975 and came under Marxist rule, Scouting was banned by that government. Scouting was started again in February 1991. In 1994, the interreligious Associação Nacional de Escuteiros and the Catholic Associação de Escuteiros Católicos de Angola merged forming the AEA.

Today, Scouting includes an inter-religious pastoral commission which brings together the main religions represented by the members of the Scout Association. Scouting enjoys special support from the Catholic Church and some groups are linked to the church, excellent relations exist with UN agencies. Together with UNICEF, Scouting has been in the forefront of the campaign for children's immunization against polio. Scouting activities focus on improving the quality of life in local communities; these include humanitarian assistance to those who have fled armed conflict, working with UNICEF on Oral Rehydration Therapy programs, an anti-polio campaign led by the Ministry of Health. The association is divided in four sections according to age: Lobitos/Lobitas - ages 7 to 10 Exploradores/Júniores - ages 10 to 14 Pioneiros/Séniores - ages 15 to 18 Caminheiros - ages 18 to 22 Cub Scout LawO Lobito escuta "Aquelá" O Lobito não se escuta a si próprioCub Scout MottoDa melhor vontade Scout LawA Honra do Escuta inspira confiança.

O Escuta é Leal. O Escuta é útil. O Escuta é amigo de todos. O Escuta é delicado e respeitador. O Escuta protege as plantas e os animais. O Escuta é obediente. O Escuta tem sempre boa disposição de espírito. O Escuta é sóbrio, económico e respeitador do bem alheio. O Escuta é nas palavras e nas acções. Scout PromisePrometo, pela minha honra e com a graça de Deus, fazer todo o possível por:Cumprir os meus deveres para com Deus, a Igreja e a Pátria. Official website

Osborne Perry Anderson

Osborne Perry Anderson was an African-American abolitionist and the only surviving African-American member of John Brown's raid on Harpers Ferry, a soldier in the Union army of the American Civil War. In 1830 Anderson was born a free African American in Pennsylvania, he completed basic schooling and attended Oberlin College in Ohio, after which he moved to Chatham in Canada West in 1850 and opened shop as a printer. This skill served him as an abolitionist. In May 1858 Anderson met John Brown and learned of the revolution that he was planning at a meeting in Chatham; because of his writing skills Anderson was appointed as the recording secretary at several of the meetings and was promoted to a member of Brown’s provisional congress. During the raid, Col. Lewis Washington, great grand-nephew of George Washington, was taken hostage by the raiders, surrendered to Anderson Frederick the Great's sword and pistols presented by General Lafayette to General Washington. John Brown brandished the sword while commanding his men at Harpers Ferry.

During the raid on Harpers Ferry Anderson was stationed with Albert Hazlett, once it became apparent to them that the raid was a failure they both retreated to Pennsylvania. Hazlett was captured and hanged. After the failed raid, Anderson went on to write an account of the events, titled A Voice From Harper’s Ferry; the book describes the conditions that were present at the Harpers Ferry raid, including the training, the supplies that were available, the events that led up to and followed the raid. In it, he claims he was the only surviving person, with Brown during the entire raid. Though Anderson did not name the friends who aided his escape in his account analysis concluded that William C. Goodridge, a conductor on the Underground Railroad, hid him in York, Pennsylvania sent him by rail to Philadelphia. Anderson proceeded from there to Canada. Upon the start of the Civil War Anderson became a noncommissioned officer of the Union Army, he died in Washington D. C. in 1872. He was interred at Columbian Harmony Cemetery.

Works by or about Osborne Perry Anderson at Internet Archive Works by Osborne Perry Anderson at LibriVox

Keechaka Vadham

Keechaka Vadham is an Indian silent film produced, directed and edited by R. Nataraja Mudaliar; the first film to have been made in South India, it was shot in five weeks at Nataraja Mudaliar's production house, India Film Company. As the members of the cast were Tamils, Keechaka Vadham is considered to be the first Tamil film. No print of it is known making it a lost film; the screenplay, written by C. Rangavadivelu, is based on an episode from the Virata Parva segment of the Hindu epic Mahabharata, focusing on Keechaka's attempts to woo Draupadi; the film stars Raju Jeevarathnam as the central characters. Released in the late 1910s, Keechaka Vadham was commercially successful and received positive critical feedback; the film's success prompted Nataraja Mudaliar to make a series of similar historical films, which laid the foundation for the South Indian cinema industry and led to his being recognised as the father of Tamil cinema. Nataraja Mudaliar's works were an inspiration to other filmmakers including Raghupathi Surya Prakasa and J. C.

Daniel. Keechaka, the commander of King Virata's forces, attempts to woo and marry Draupadi by any means necessary; when Keechaka meets Draupadi, she requests him to rendezvous with her at a secret hiding place. He arrives only to find Bhima instead of Draupadi. Raju Mudaliar as Keechaka Jeevarathnam as Draupadi R. Nataraja Mudaliar, a car dealer, based in Madras, developed an interest in motion pictures after watching Dadasaheb Phalke's 1913 mythological film, Raja Harishchandra at the Gaiety theatre in Madras; the former learned the basics of photography and filmmaking from Stewart Smith, a Poona-based British cinematographer who had worked on a documentary that chronicled the viceroyship of Lord Curzon. Nataraja Mudaliar bought a Williamson 35 mm camera and printer from Mooppanar, a wealthy landowner based in Thanjavur, for ₹1,800. In 1915, he established the India Film Company, South India's first production company, he set up a film studio on Miller's Road in Purasawalkam with the help of business associates who invested in his production house.

Nataraja Mudaliar sought advice from his friend, theatrical artist Pammal Sambandha Mudaliar, who suggested that he depict the story of Draupadi and Keechaka from the Virata Parva segment of the Hindu epic Mahabharata. Some of Nataraja Mudaliar's relatives objected, feeling that it was an inappropriate story for his debut venture, but Sambandha Mudaliar persuaded him to proceed with making the film as audiences were familiar with the story. Attorney C. Rangavadivelu, a close friend of Nataraja Mudaliar, assisted him in writing the screenplay as the latter was not a writer by profession; the paintings of Raja Ravi Varma provided Nataraja Mudaliar with a source of inspiration for recreating the story on celluloid. Nataraja Mudaliar cast stage actors Raju Mudaliar and Jeevarathnam as Keechaka and Draupadi, respectively. Keechaka Vadham was filmed on a budget of ₹35,000, quite expensive at the time. Principal photography began in 1916–1917, the film was shot over 35–37 days. Nataraja Mudaliar imported the film stock London with the help of an Englishman named Carpenter, who worked for the Bombay division of the photographic technology company, Kodak.

Film historian Randor Guy noted in his 1997 book Starlight Starbright: The Early Tamil Cinema that a thin white piece of cloth was used as a ceiling for filming and sunlight was filtered through it onto the floor. Rangavadivelu was experienced in playing female roles on stage for the Suguna Vilasa Sabha, coached the artists on set; the film's production and editing were handled by Nataraja Mudaliar himself. The film was shot with a speed of 16 frames per second, the standard rate for a silent film, at the India Film Company, with intertitles in English and Hindi; the Tamil and Hindi intertitles were written by Sambandha Mudaliar and Devdas Gandhi while Nataraja Mudaliar wrote the English intertitles himself with the assistance of Guruswami Mudaliar and Thiruvengada Mudaliar, a professor from Pachaiyappa's College. Keechaka Vadham was the first film made in South India. According to Guy, Nataraja Mudaliar established a laboratory in Bangalore to process the film negatives since there was no film laboratory in Madras.

Nataraja Mudaliar believed that Bangalore's colder climate "would be kind to his exposed film stock". The film's final reel length was 6,000 ft. According to Muthiah, Keechaka Vadham was first released at the Elphinstone Theatre in Madras; the film yielded ₹15,000, which Muthiah noted to be a "tidy profit in those days." Writer Firoze Rangoonwalla notes that a reviewer for The Mail praised the film: "It has been prepared with great care and is drawing full houses". Guy pointed out that with the film's critical and commercial success, Nataraja Mudaliar had "created history". Since no print is known to have survived, this makes it a lost film. Keechaka Vadham's success inspired Nataraja Mudaliar to make a series of historical films: Draupadi Vastrapaharanam, Lava Kusa, Shiva Leela, Rukmini Satyabhama and Mahi Ravana, he retired from filmmaking in 1923 after a fire destroyed his production house. Nataraja Mudaliar is regarded


Kodumanal is a village located in the Erode district in the southern Indian state of Tamil Nadu. It was once a flourishing ancient trade city known as Kodumanam, as inscribed in Patittrupathu of Sangam Literature; the place is an important archaeological site, under the control of State Archaeological Department of Tamil Nadu. It is located on the northern banks of a tributary of the Cauvery; the inhabitants of this destroyed ancient city of Chera dynasty were skilled craftsmen, who were specialized in making beads and high-quality iron. The place is referred to in Sangam literature as an important industrial centre that had links with the Chola port city of Kaveripoompattinam, now called Poompuhar; the city played a major role in Indo-Roman trade and relations, as the ancient city is located on the mid-way of a Roman trade route, linking Muziris port on the Malabar Coast with the Kaveripoompattinam Port in the Coromandel Coast. Excavations have been carried out and it came out with the layers of a megalithic-cum-early tombs of historic period.

There were two female and one male human skeleton were recovered from a pit burial in this site. A set of 300 megalithic tombs of different types and sizes were recorded in this area; the ancient city has been destroyed in time and now the area is available with the remains of a megalithic settlement dating back to the 2nd century BC. This was the centre for the Romans who visited to obtain beryls from Kodumanal; the megalithic communities that flourished in this site belong to the period of 2nd century BC to 2nd century AD. The iron and steel furnaces and iron artefacts produced in these places revealed the technical advancement made by the iron smelters around 500 BC; the excavated sword bit contained spheroidal graphite phase and forge welding of high-carbon cutting edge. This place was once celebrated for its trade in precious stones like garnet, lapis lazuli and quartz; the people of this city were experts in manufacturing the finest iron. Excavations uncovered ancient iron objects such as arrow swords.

They produced Roman artefacts, iron melting furnaces, shell bangles and pottery with the Tamizhi scripts. Other artifacts uncovered during the excavation of this site include roulette pottery, Roman silver coins, gold and silver spirals. A bronze statue of a lion and the iron melting furnaces were important to deciphering the site's history. Https://