Uniform distribution on the sphere and caps

TL;DR

This paper investigates conditions under which the behavior of point sequences on spherical caps implies their uniform distribution on the entire sphere.

Contribution

It introduces criteria linking local cap behavior to global uniform distribution on the sphere.

Findings

Established conditions for uniform distribution based on cap behavior

Connected local cap properties with global distribution patterns

Provided theoretical insights into spherical point distributions

Abstract

In this note we will consider the question when from the appropriate behavior of a sequence of points on caps we can conclude that the sequence is uniformly distributed on the sphere.