Abstract
Let ℋ be a metric space with metric ϱ(x, y), 𝓑 be the σ-algebra of its Borel subsets, 𝓒ℋbe the space of all bounded continuous functions defined on ℋ with the norm \( {\left\| f \right\|_x} = \mathop{{\sup }}\limits_x \left| {f(x)} \right| \). A sequence of measures μ n defined on 𝓑 is called weakly convergent to measure μ if for any function f in 𝓒ℋ the relation
is satisfied. The set M of measures {μ} defined on 𝓑 is called weakly compact if from any sequence of measures μ n in M a weakly convergent subsequence can be extracted.
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© 2004 Springer-Verlag Berlin Heidelberg
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Gihman, I.I., Skorokhod, A.V. (2004). Limit Theorems for Random Processes. In: The Theory of Stochastic Processes I. Classics in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61943-4_6
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DOI: https://doi.org/10.1007/978-3-642-61943-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20284-4
Online ISBN: 978-3-642-61943-4
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