# Existence and Continuity of Differential Entropy for a Class of Distributions

## TL;DR

This paper identifies a class of distributions for which differential entropy is uniformly convergent under total variation distance, providing a practical way to verify entropy properties across this class.

## Contribution

It introduces a new class of distributions with verifiable conditions ensuring uniform convergence of differential entropy.

## Key findings

- Differential entropy converges uniformly over the class under total variation.
- The class's conditions are easy to verify for specific distributions.
- Provides theoretical foundation for entropy analysis in continuous distributions.

## Abstract

In this paper, we identify a class of absolutely continuous probability distributions, and show that the differential entropy is uniformly convergent over this space under the metric of total variation distance. One of the advantages of this class is that the requirements could be readily verified for a given distribution.