Distributions that arise as derivatives of families of measures

TL;DR

This paper characterizes the distributions that can be obtained as derivatives of families of probability measures and signed measures on smooth manifolds, providing a mathematical framework for understanding their structure.

Contribution

It introduces a comprehensive characterization of distributions as derivatives of measure families on smooth manifolds, expanding theoretical understanding.

Findings

Identifies conditions under which distributions are derivatives of measure families

Provides a mathematical framework for derivatives of measures on manifolds

Enhances understanding of measure derivatives in geometric contexts

Abstract

We characterize the distributions that arise as derivatives of families of probabilities and of positive and signed measures on smooth manifolds.