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Kolmogorov Integral
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., the Kolmogorov integral (or Kolmogoroff integral) is a generalized integral introduced by including the Lebesgue–Stieltjes integral, the Burkill integral, and the Hellinger integral as special cases. The integral is a limit over a directed family of partitions, when the resulting limiting value is independent of the tags of each partition segment. References * * {{integral Definitions of mathematical integration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burkill Integral
In mathematics, the Burkill integral is an integral introduced by for calculating areas. It is a special case of the Kolmogorov integral In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in mode .... References * * * Definitions of mathematical integration {{mathanalysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hellinger Integral
In mathematics, the Hellinger integral is an integral introduced by that is a special case of the Kolmogorov integral. It is used to define the Hellinger distance In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of ''f''-divergence. The Hellin ... in probability theory. References * * * {{integral Definitions of mathematical integration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück, and Nigel Hitchin. Currently, the managing editor of Mathematische Annalen is Thomas Schick. Volumes 1–80 (1869–1919) were published by Teubner. Since 1920 (vol. 81), the journal has been published by Springer. In the late 1920s, under the editorship of Hilbert, the journal became embroiled in controversy over the participation of L. E. J. Brouwer on its editorial board, a spillover from the foundational Brouwer–Hilbert controversy. Between 1945 and 1947 the journal briefly ceased publication. References External links''Mathematische Annalen''homepage at Springer''Mathematische Annalen''archive (1869†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
