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Journal of Logic and Analysis, 2020 The coordinates along any fixed direction(s), of points on the sphere $S^{n-1}(\sqrt{n})$, roughly follow a standard Gaussian distribution as $n$ approaches infinity. We revisit this classical result from a nonstandard analysis perspective, providing a new proof by working with hyperfinite dimensional spheres.
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MATRIX POWER MEANS AND PÓLYA--SZEGÖ TYPE INEQUALITIES [PDF]
Surveys in Mathematics and its Applications, 2020 t has been shown that if μ is a compactly supported probability measure on Mn+, then for every unit vector η∈ℂn, there exists a compactly supported probability measure (denoted by on ℝ+ so that the inequality ≤ Pt() (t∈(0,1]) holds. In particular,
Mohsen Kian , Fatemeh Rashid
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Using the quantum probability ranking principle to rank interdependent documents [PDF]
, 2010 A known limitation of the Probability Ranking Principle (PRP) is that it does not cater for dependence between documents. Recently, the Quantum Probability Ranking Principle (QPRP) has been proposed, which implicitly captures dependencies between ...
Azzopardi, L. +5 more
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On orthogonal probability measures [PDF]
Proceedings of the American Mathematical Society, 1953 Definitions. Let X be an arbitrary set, f( a Borel-field of some subsets B of X, and W(t) the family of all probability measures defined on C, i.e. the totality of all countably additive, non-negative set functions m(B), B Ez, for which m(X) = 1. Henceforth the word "measure" denotes an element of 2W(1) and the expression "set of measures" a subset of ...
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A Joint Limit Theorem for Laplace Transforms of the Riemann Zeta–Function
Nonlinear Analysis, 2007 In the paper, a joint limit theorem in the sense of weak convergence of probability measures on the complex plane for Laplace transforms of the Riemann zetafunction is obtained.
A. Laurinčikas
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Вестник Самарского университета: Естественнонаучная серия, 2023 In this short communication we prove that the subspace Pn,n−1(X)of all probability measures P(X), whose supports consist of exactly n points is an (n−1)-dimensional topological manifold.
Mikhail V. Dolgopolov +1 more
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Distinguishability of Probability Measures
The Annals of Mathematical Statistics, 1969 Independent identically distributed observations, $X_1, X_2, \cdots$, are taken sequentially. All that is known a priori about their common probability measure, $P$, is that it is a member of a given (at most countable) family, $\pi = \{P_n\}^\infty_{n=1}$, of such measures.
Fisher, Lloyd, Ness, John W. Van
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Measure and probability in cosmology
Physical Review D, 2012 43 pages, 2 ...
Schiffrin, Joshua S., Wald, Robert M.
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A two-dimensional limit discrete theorem for Mellin transforms of the Riemann zeta-function
Lietuvos Matematikos Rinkinys, 2007 In the paper two-dimensional limit theorem for the modified Mellin transform of the Riemann zeta-function is obtained.
Violeta Balinskaitė
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Theoretical Computer Science, 1989 Probability measures on words are studied in their relation with coding and finite automata. We continue the exploration of this borderline area and present some new results. We particularly insist on the notion of a rational probability measure which, although perhaps not quite new, has not yet received all the attention it deserves.
Georges Hansel, Dominique Perrin
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