Some Proofs on Statistical Magnitudes for Continuous Phenomena

TL;DR

This paper provides mathematical proofs for the continuity of key statistical measures like disequilibrium, Shannon information, and complexity in continuous systems, and discusses the existence of Shannon information in such contexts.

Contribution

It offers new rigorous proofs for the continuity of statistical magnitudes and explores the existence of Shannon information in continuous phenomena.

Findings

Proves continuity of disequilibrium, Shannon information, and complexity in distribution spaces.

Establishes conditions for the existence of Shannon information in continuous systems.

Provides mathematical foundations for analyzing continuous statistical measures.

Abstract

In this work, the proofs concerning the continuity of the disequilibrium, Shannon information and statistical complexity in the space of distributions are presented. Also, some results on the existence of Shannon information for continuous systems are given.