Information Theory for Expectation Measures (2501.17554v1)

Abstract: Shannon based his information theory on the notion of probability measures as it we developed by Kolmogorov. In this paper we study some fundamental problems in information theory based on expectation measures. In the theory of expectation measures it is natural to study data sets where no randomness is present and it is also natural to study information theory for point processes as well as sampling where the sample size is not fixed. Expectation measures in combination with Kraft's Inequality can be used to clarify in which cases probability measures can be used to quantify randomness.