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arXiv · 1606.02848

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

Matija Vidmar
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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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Matija Vidmar. 2017-06-26. A couple of remarks on the convergence of $σ$-fields on probability spaces. https://arxiv.org/abs/1606.02848

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