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A note on the von Weizs\"{a}cker theorem

Probability 2025-11-21 v2

Abstract

The von Weizs\"{a}cker theorem states that every sequence of nonnegative random variables has a subsequence which is Ces\`{a}ro convergent to a nonnegative random variable which might be infinite. The goal of this note is to provide a description of the set where the limit is finite. For this purpose, we use a decomposition result due to Brannath and Schachermayer.

Keywords

Cite

@article{arxiv.2001.11727,
  title  = {A note on the von Weizs\"{a}cker theorem},
  author = {Stefan Tappe},
  journal= {arXiv preprint arXiv:2001.11727},
  year   = {2025}
}

Comments

7 pages

R2 v1 2026-06-23T13:26:15.420Z