A couple of remarks on the convergence of σ-fields on probability spaces

2016/06/09 by Matija Vidmar, Vidmar, Matija
Mathematics · #46B28 #60A05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:46B28 #msc:60A05

paper · pdf · doi:10.48550/arxiv.1606.02848

10 pages, 1 figure

arxiv created 2017/06/26 · arxiv updated 2017/06/27

Abstract

The following modes of convergence of sub-σ-fields on a given probability space have been studied in the literature: weak convergence, strong convergence, convergence with respect to the Hausdorff metric, almost-sure convergence, set-theoretic convergence, monotone convergence. It is noted that all preserve independence, and all are invariant under passage to an equivalent probability measure. Partial results for the case of operator-norm convergence obtain.

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