Functions and Analysis

   

A General Form of the Beppo Levi`s Lemma

Authors: Johan Aspegren

In this article we will prove a version of the Beppo Levi`s lemma for the complex valued functions. This achieved by making a more stronger asumption that is assumed in Beppo Levi`s lemma. We will assume that the sum of measurable functions that is absolutely convergent almost everywhere is integrable. We will prove that it implies the asumptions of the Beppo Levi lemma, if we consider functions that are non-negative. It can be argued that our version is more suitable to applications, and we will prove a new probability law. We will show that with our asumptions in probability theory it follows that the expected value is countable additive. Moreover, it follows that in strong law of large numbers we don`t need to make any asumptions on distributions and the mean of the sample will convergence almost surely to the mean of the expected values.

Comments: 5 Pages.

Download: PDF

Submission history

[v1] 2019-09-15 05:41:14
[v2] 2019-09-16 03:56:42

Unique-IP document downloads: 32 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus