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On the Weak Convergence of Probability Measures in Orlicz Spaces
Theory of Probability and Its Applications, 1996Necessary and sufficient conditions for weak convergence of probability measures in separable Orlicz spaces in terms of characteristic functionals and norm moments are given.
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, 2018 This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and ...
Bogachev, Vladimir I
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Journal of the American Statistical Association, 1985
Etant donné un espace de probabilité (\(\Omega\),\({\mathcal F},P)\), on considère une famille (\({\mathcal X}_{\omega})_{\omega \in \Omega}\) d'ensembles et \({\bar \Omega}=\cup_{\omega}\{\omega \}\times {\mathcal X}_{\omega}\), on se donne une famille \({\mathcal U}=\{(f_ i)_{i\in I_ 0}\}\) de fonctions de \({\bar \Omega}\) dans \({\mathbb{R ...
David Pollard, Harald Bergstrom
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Etant donné un espace de probabilité (\(\Omega\),\({\mathcal F},P)\), on considère une famille (\({\mathcal X}_{\omega})_{\omega \in \Omega}\) d'ensembles et \({\bar \Omega}=\cup_{\omega}\{\omega \}\times {\mathcal X}_{\omega}\), on se donne une famille \({\mathcal U}=\{(f_ i)_{i\in I_ 0}\}\) de fonctions de \({\bar \Omega}\) dans \({\mathbb{R ...
David Pollard, Harald Bergstrom
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Weak convergence of probability measures in spaces of smooth functions
Stochastic Processes and Their Applications, 1986 A large number of results are available about the weak convergence of probability measures in spaces of continuous functions and spaces of cadlag functions.
Richard J Wilson
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On Weak Convergence of Gaussian Measures
Theory of Probability & Its Applications, 1988See the review in Zbl 0641.60004.
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2012
In this chapter we consider the fundamental concept of weak convergence of probability measures. This will lay the groundwork for the precise formulation of the Central Limit Theorem and other Limit Theorems of probability theory (see Chap. 10).
Leonid Koralov, Yakov G. Sinai
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In this chapter we consider the fundamental concept of weak convergence of probability measures. This will lay the groundwork for the precise formulation of the Central Limit Theorem and other Limit Theorems of probability theory (see Chap. 10).
Leonid Koralov, Yakov G. Sinai
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2009
We shall now prove Vitali’s Theorem 3.10 and Theorem 3,11. As we noted in the remark after the statement of Theorem 3.11, Vi tali’s results give non-trivial necessary and sufficient conditions in order that $$\mathop {\lim }\limits_n \int\limits_x {|{f_n} - f|d\mu = 0} $$ (6.1) , where (X, 𝒜, µ) is a measure space and \( \left\{ {{f_n}:n = 1,
John J. Benedetto, Wojciech Czaja
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We shall now prove Vitali’s Theorem 3.10 and Theorem 3,11. As we noted in the remark after the statement of Theorem 3.11, Vi tali’s results give non-trivial necessary and sufficient conditions in order that $$\mathop {\lim }\limits_n \int\limits_x {|{f_n} - f|d\mu = 0} $$ (6.1) , where (X, 𝒜, µ) is a measure space and \( \left\{ {{f_n}:n = 1,
John J. Benedetto, Wojciech Czaja
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Weak convergence of vector measures
Publicationes Mathematicae Debrecen, 1994Summary: We consider a notion of weak convergence for measures taking values in a Banach space. A version of Prokhoroff's Theorem is proved for such measures, and applications are given to the existence of products of measures with values in a Banach algebra and to a Strassen's Theorem for measures taking values in the positive cone of a Banach lattice.
März, Michael, Shortt, R. M.
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