A Strong Law of Large Numbers for Positive Random Variables
Abstract
In the spirit of the famous KOML\'OS (1967) theorem, every sequence of nonnegative, measurable functions \ fn \n ∈ on a probability space, contains a subsequence which - along with all its subsequences - converges a.e. in CES\`ARO mean to some measurable f* : [0, ∞]. This result of VON WEIZS\"ACKER (2004) is proved here using a new methodology and elementary tools; these sharpen also a theorem of DELBAEN & SCHACHERMAYER (1994), replacing general convex combinations by CES\`ARO means.
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