The almost sure behavior of certain spatial repartitions of local empirical processes indexed by functions

TL;DR

This paper studies the almost sure behavior of specific spatial repartitions of local empirical processes indexed by functions, focusing on their weak convergence properties.

Contribution

It introduces new insights into the almost sure behavior of spatial repartitions of local empirical processes, expanding understanding of their weak convergence.

Findings

Characterization of almost sure convergence

Conditions for weak convergence of local empirical processes

Theoretical framework for spatial repartitions

Abstract

We investigate a particular form of weak convergence of the local empirical process.