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on which two structures are given — a group structure and a topology, such that the group operations are continuous. Specifically, th
14 KB (2,197 words) - 16:40, 31 March 2020
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...es of decision-making, used in [[Operations research|operations research]] and game theory (cf. [[Games, theory of|Games, theory of]]). It is implicit in
9 KB (1,423 words) - 08:07, 6 June 2020
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...stic assigned to planar figures of a certain class (for example, polygons) and having the following properties: 1) the area is non-negative; 2) the area i
21 KB (3,223 words) - 18:48, 5 April 2020
...t of convergence arises, for example, in the study of mathematical objects and their approximation by simpler objects. Thus, in order to calculate the are
...e to calculate this solution with the required accuracy. Both for ordinary and partial differential equations there are various convergent difference meth
22 KB (3,726 words) - 10:31, 2 September 2017
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...which boundary properties of functions are studied in terms of topological and metric properties of various cluster sets.
25 KB (3,728 words) - 09:43, 26 March 2023
...iven series) of some [[Linear topological space|linear topological space]] and a certain infinite set of their partial sums (called the partial sums of th
and $ \{ s _{n} \} $
29 KB (4,393 words) - 19:21, 27 January 2020
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...$ and let $d \sigma _ { r }$ be the normalized [[Lebesgue measure|Lebesgue measure]] on $S ( x , r )$. One version of the classical converse of Gauss' mean-va
17 KB (2,607 words) - 16:38, 2 February 2024
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...white noise analysis has developed into a viable framework for stochastic and infinite-dimensional analysis [[#References|[a4]]]–[[#References|[a6]]],
27 KB (3,916 words) - 19:20, 13 January 2024
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and the vector $ k _ {M} $.
18 KB (2,636 words) - 08:00, 13 May 2022
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...on of a non-linear differential equation with a Gaussian white noise input and an observation process whose differential is a non-linear function of the s
9 KB (1,283 words) - 17:44, 1 July 2020
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unknowns $ p = ( p _ {1} \dots p _ {n} ) $ ("generalized momenta") and $ q = ( q _ {1} \dots q _ {n} ) $ ("generalized coordinates"), of the for
13 KB (1,837 words) - 07:56, 21 January 2024
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and let $ p $
20 KB (3,020 words) - 17:24, 6 January 2024
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and the independent observations $ \phi $
13 KB (1,879 words) - 11:25, 31 January 2022
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...eories, in string theory, where both kinds of transformations are present, and in two-dimensional conformal field theories.
27 KB (3,739 words) - 06:51, 26 March 2023
...e quotient space $\Gamma\setminus G$ has finite volume in the sense of the measure induced by the left-invariant
[[Haar measure|Haar measure]] on the group $G$. The concept of lattices includes that of uniform discre
20 KB (3,146 words) - 02:52, 23 July 2018
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with respect to the Lebesgue measure $ dV $.
10 KB (1,514 words) - 07:41, 26 March 2023
...uthor(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Alike Lic
in the area of probability and statistics.
11 KB (1,737 words) - 12:11, 23 November 2023
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where the integral is taken with respect to the Haar measure.
11 KB (1,730 words) - 19:04, 9 January 2024
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...onnection with work on the construction of atomic reactors, J. von Neumann and S. Ulam suggested using the apparatus of probability theory in the computer
24 KB (3,433 words) - 13:09, 13 January 2024
...ucted analogously. A further generalization leads to Fourier coefficients and Fourier series for elements of a Hilbert space.
...r series in the trigonometric system has been most thoroughly developed, and these were the first examples of Fourier series. If one has in mind Fourie
21 KB (3,473 words) - 19:50, 26 April 2012