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Nikodym
Otto Marcin Nikodym (3 August 1887 – 4 May 1974) (also Otton Martin Nikodým) was a Polish mathematician. Education and career Nikodym studied mathematics at the University of Jan Kazimierz (UJK) in Lvov (today's University of Lviv). Immediately after his graduation in 1911, he started his teaching job at a high school in Kraków where he remained until 1924. He eventually obtained his doctorate in 1925 from the University of Warsaw; he also spent an academic year (1926-1927) in Sorbonne. Nikodym taught at the Jagiellonian University in Kraków and University of Warsaw and at the Akademia Górnicza in Kraków in the years that followed. He moved to the United States in 1948 and joined the faculty of Kenyon College. He retired in 1966 and moved to Utica, New York, where he continued his research until retirement. Personal life Nikodym was born in 1887 in Demycze, a suburb of Zabłotów (in modern day Ukraine), to a family with Polish, Czech, Italian and French roots. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radon–Nikodym Theorem
In mathematics, the Radon–Nikodym theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable space. A ''measure'' is a set function that assigns a consistent magnitude to the measurable subsets of a measurable space. Examples of a measure include area and volume, where the subsets are sets of points; or the probability of an event, which is a subset of possible outcomes within a wider probability space. One way to derive a new measure from one already given is to assign a density to each point of the space, then integrate over the measurable subset of interest. This can be expressed as :\nu(A) = \int_A f \, d\mu, where is the new measure being defined for any measurable subset and the function is the density at a given point. The integral is with respect to an existing measure , which may often be the canonical Lebesgue measure on the real line or the ''n''-dimensional Euclidean space (corresponding to our s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanisława Nikodym
Stanisława Nikodym (née Liliental; 2 July 1897 — 25 March 1988) was a Polish mathematician and artist. She is known for her results in continuum theory, especially on Jordanian continuums. Life Stanisława Dorota Liliental was born in Warsaw to Regina Lilientalowa, an ethnographer, and Nathan Liliental. Stanisława had a younger brother, Antoni (born 1908). She attended Helena Skłodowska-Szalay's primary school, and went to Warsaw's private school for women for 7 years. She joined the Warsaw University in 1916, reading mathematics under Stefan Mazurkiewicz, Zygmunt Janiszewski, and Wacław Sierpiński She married Otto M. Nikodym, a mathematician, in 1924, and joined him at Krakow. Supervised by Mazurkiewicz, she was awarded a doctoral degree from the Jagiellonian University in 1925. She was the first woman in Poland to obtain a PhD in mathematics. Receiving government funding to study in Paris, she and Otto attended the Sorbonne for two years from 1926. In 1930, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radon–Nikodym Property
In mathematics, the Bochner integral, named for Salomon Bochner, extends the definition of Lebesgue integral to functions that take values in a Banach space, as the limit of integrals of simple functions. Definition Let (X, \Sigma, \mu) be a measure space, and B be a Banach space. The Bochner integral of a function f : X \to B is defined in much the same way as the Lebesgue integral. First, define a simple function to be any finite sum of the form s(x) = \sum_^n \chi_(x) b_i where the E_i are disjoint members of the \sigma-algebra \Sigma, the b_i are distinct elements of B, and χE is the characteristic function of E. If \mu\left(E_i\right) is finite whenever b_i \neq 0, then the simple function is integrable, and the integral is then defined by \int_X \left sum_^n \chi_(x) b_i\right, d\mu = \sum_^n \mu(E_i) b_i exactly as it is for the ordinary Lebesgue integral. A measurable function f : X \to B is Bochner integrable if there exists a sequence of integrable simple functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikodym Set
In mathematics, a Nikodym set is a subset of the unit square in \mathbb^2 with complement of Lebesgue measure zero, such that, given any point in the set, there is a straight line that only intersects the set at that point. The existence of a Nikodym set was first proved by Otto Nikodym in 1927. Subsequently, constructions were found of Nikodym sets having continuum many exceptional lines for each point, and Kenneth Falconer found analogues in higher dimensions. Nikodym sets are closely related to Kakeya sets (also known as Besicovitch sets). The existence of Nikodym sets is sometimes compared with the Banach–Tarski paradox. There is, however, an important difference between the two: the Banach–Tarski paradox relies on non-measurable sets. Mathematicians have also researched Nikodym sets over finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stefan Banach
Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern functional analysis, and an original member of the Lwów School of Mathematics. His major work was the 1932 book, ''Théorie des opérations linéaires'' (Theory of Linear Operations), the first monograph on the general theory of functional analysis. Born in Kraków to a family of Goral descent, Banach showed a keen interest in mathematics and engaged in solving mathematical problems during school recess. After completing his secondary education, he befriended Hugo Steinhaus, with whom he established the Polish Mathematical Society in 1919 and later published the scientific journal ''Studia Mathematica''. In 1920, he received an assistantship at the Lwów Polytechnic, subsequently becoming a professor in 1922 and a member of the Polish Academy of Learning in 1924. Ban ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zabolotiv
Zabolotiv ( ua, Заболотів, pl, Zabłotów, yi, זאַבלאטאוו ''Zablotov'') is an urban-type settlement in Kolomyia Raion of Ivano-Frankivsk Oblast in Western Ukraine. It hosts the administration of Zabolotiv urban hromada, one of the hromadas of Ukraine. Population: . In 2001, the population was 4,129. History Starting from 1790, a growing Jewish community became an important part of local life. At the beginning of the 20th century, antisemitic unrest culminated in the first pogrom in Zabolotiv in 1903. Later, German Nazis exterminated one part of the Jewish population while others managed to flee to the United States and Israel. Until 18 July 2020, Zabolotiv belonged to Sniatyn Raion. The raion was abolished in July 2020 as part of the administrative reform of Ukraine, which reduced the number of raions of Ivano-Frankivsk Oblast to six. The area of Sniatyn Raion was merged into Kolomyia Raion. Notable people * Otto M. Nikodym (1887–1974) (Otton Mar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zabłotów
Zabolotiv ( ua, Заболотів, pl, Zabłotów, yi, זאַבלאטאוו ''Zablotov'') is an urban-type settlement in Kolomyia Raion of Ivano-Frankivsk Oblast in Western Ukraine. It hosts the administration of Zabolotiv urban hromada, one of the hromadas of Ukraine. Population: . In 2001, the population was 4,129. History Starting from 1790, a growing Jewish community became an important part of local life. At the beginning of the 20th century, antisemitic unrest culminated in the first pogrom in Zabolotiv in 1903. Later, German Nazis exterminated one part of the Jewish population while others managed to flee to the United States and Israel. Until 18 July 2020, Zabolotiv belonged to Sniatyn Raion. The raion was abolished in July 2020 as part of the administrative reform of Ukraine, which reduced the number of raions of Ivano-Frankivsk Oblast to six. The area of Sniatyn Raion was merged into Kolomyia Raion. Notable people * Otto M. Nikodym (1887–1974) (Otton Martin Ni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utica, New York
Utica () is a city in the Mohawk Valley and the county seat of Oneida County, New York, United States. The tenth-most-populous city in New York State, its population was 65,283 in the 2020 U.S. Census. Located on the Mohawk River at the foot of the Adirondack Mountains, it is approximately west-northwest of Albany, east of Syracuse and northwest of New York City. Utica and the nearby city of Rome anchor the Utica–Rome Metropolitan Statistical Area comprising all of Oneida and Herkimer Counties. Formerly a river settlement inhabited by the Mohawk Nation of the Iroquois Confederacy, Utica attracted European-American settlers from New England during and after the American Revolution. In the 19th century, immigrants strengthened its position as a layover city between Albany and Syracuse on the Erie and Chenango Canals and the New York Central Railroad. During the 19th and 20th centuries, the city's infrastructure contributed to its success as a manufacturing cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jagiellonian University Faculty
The Jagiellonian dynasty (, pl, dynastia jagiellońska), otherwise the Jagiellon dynasty ( pl, dynastia Jagiellonów), the House of Jagiellon ( pl, Dom Jagiellonów), or simply the Jagiellons ( pl, Jagiellonowie), was the name assumed by a cadet branch of the Lithuanian ducal dynasty of Gediminids upon reception by Jogaila, the Grand Duke of Lithuania, of baptism as Władysław in 1386, which paved the way to his ensuing marriage to the Queen Regnant Jadwiga of Poland, resulting in his ascension to the Crown of the Kingdom of Poland as Władysław II Jagiełło (initially ruling ''jure uxoris'' jointly with Hedwig until her death), and the effective promotion of his branch to a royal dynasty. The Jagiellons reigned in several Central European countries between the 14th and 16th centuries. Members of the dynasty were Kings of Poland (1386–1572), Grand Dukes of Lithuania (1377–1392 and 1440–1572), Kings of Hungary (1440–1444 and 1490–1526), and Kings of Bohemia and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". Universities typically offer both undergraduate and postgraduate programs. The first universities in Europe were established by Catholic Church monks. The University of Bologna (), Italy, which was founded in 1088, is the first university in the sense of: *being a high degree-awarding institute. *using the word ''universitas'' (which was coined at its foundation). *having independence from the ecclesiastic schools and issuing secular as well as non-secular degrees (with teaching conducted by both clergy and non-clergy): grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Warsaw Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". Universities typically offer both undergraduate and postgraduate programs. The first universities in Europe were established by Catholic Church monks. The University of Bologna (), Italy, which was founded in 1088, is the first university in the sense of: *being a high degree-awarding institute. *using the word ''universitas'' (which was coined at its foundation). *having independence from the ecclesiastic schools and issuing secular as well as non-secular degrees (with teaching conducted by both clergy and non-clergy): grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hilde' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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