Information and σ-algebras

Abstract

In this work, we clarify the relationship between the information that an agent receives from a signal, from an experiment or from his own ability to determine the true state of nature that occurs and the information that an agent receives from a σ-algebra. We show that, for countably generated σ-algebras, the larger it is, the larger the information is. The same is true for general σ-algebras after the removal of a negligible set of states.