位相ベクトル空間における確率収束

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  • イソウ ベクトル クウカン ニ オケル カクリツ シュウソク
  • Convergence in Probability for Random Variables with Values in a Topological Vector Space

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Let (Xn) be a sequence of random variables with values in a topological vector space. We introduce the notion of convergence in probability for (Xn) and discuss the basic relations between convergence in probability and almost sure convergence. Moreover, we also defne the Cauchy property for (Xn) and prove that, if the topological vector space is complete, locally bounded and locally convex, then (Xn) has an a.s. convergent subsequence.

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