Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A Strong Law of Large Numbers for Positive Random Variables (2111.15469v2)

Published 30 Nov 2021 in math.PR

Abstract: In the spirit of the famous KOML\'OS (1967) theorem, every sequence of nonnegative, measurable functions ${ f_n }{n \in \N}$ on a probability space, contains a subsequence which - along with all its subsequences - converges a.e. in CES`ARO mean to some measurable $f* : \Omega \to [0, \infty]$. 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.

Summary

We haven't generated a summary for this paper yet.