Temporo-spatial differentiations with respect to finite unions of balls

TL;DR

This paper investigates the behavior of temporo-spatial differentiation with finite unions of balls, establishing convergence results and constructing pathological examples, highlighting the prevalence of such irregularities under certain conditions.

Contribution

It introduces new convergence results and constructs pathological examples of temporo-spatial differentiation with prescribed limit sets, expanding understanding of irregular differentiation behaviors.

Findings

Established several convergence results for temporo-spatial differentiation.

Constructed pathological examples with prescribed limit points.

Demonstrated the commonality of irregular differentiations under specific properties.

Abstract

Here we study temporo-spatial differentiation problems with respect to sequences of finite unions of balls. We establish several convergence results, as well as construct pathological temporo-spatial differentiations with prescribed sets of limit points. We also demonstrate the prevalence of certain pathological temporo-spatial differentiations in the presence of a specification-like property.