On a new measure on infinite dimensional unite cube

TL;DR

This paper introduces a novel measure on the infinite-dimensional unit cube that differs from traditional Haar and product measures, providing new insights into measure theory in infinite dimensions.

Contribution

A new measure on the infinite-dimensional unit cube is constructed, expanding the tools available beyond Haar and product measures.

Findings

The new measure is explicitly constructed.

Differences between the new measure and the product measure are analyzed.

Potential implications for infinite-dimensional analysis are discussed.

Abstract

In the article a new measure in infinite dimensional unite cube different from the Haar or product measures is constructed. Some differences between introduced measure and the product measure are discussed.