# The Classical Theorems of Measure Theory in connection with the Statistical convergence and some remarks on Steinhaus' Theorem

## TL;DR

This paper explores the relationship between classical measure theory theorems and statistical convergence, focusing on Steinhaus' theorem and the validity of measure-theoretic results under statistical limits.

## Contribution

It investigates how classical measure theory theorems extend or adapt to the context of statistical convergence, providing new insights into their applicability.

## Key findings

- Steinhaus' theorem holds under certain statistical convergence conditions
- Classical measure theorems may require modifications for statistical limits
- The paper offers remarks on the limitations and extensions of measure theory in this context

## Abstract

We study Steinhaus' theorem regarding statistical limits of measurable real valued functions and we examine the validity of the classical theorems of Measure Theory for statistical convergences.