Motivic Information

TL;DR

This paper develops a theoretical framework for defining and analyzing notions of information, entropy, and information loss within the context of motivic measures, extending classical information theory concepts.

Contribution

It introduces motivic analogs of information and entropy, establishing properties similar to classical measures on finite sets, advancing the mathematical understanding of motivic measures.

Findings

Motivic measures have well-defined notions of information and entropy.

These notions satisfy properties analogous to classical information theory.

The framework extends classical concepts to a motivic setting.

Abstract

We introduce notions of information/entropy and information loss associated to exponentiable motivic measures. We show that they satisfy appropriate analogs to the Khinchin-type properties that characterize information loss in the context of measures on finite sets.