Irregularities of distribution for bounded sets and half-spaces

TL;DR

This paper establishes a general theoretical result concerning the irregularities of distribution when intersecting Borel sets with bounded measurable sets or affine half-spaces, advancing understanding in measure theory.

Contribution

It introduces a new general theorem on distribution irregularities for Borel sets intersected with bounded sets or half-spaces, expanding prior theoretical frameworks.

Findings

Provides a unified approach to distribution irregularities

Extends classical results to broader classes of sets

Offers new bounds or estimates for irregularities

Abstract

We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.