Information and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\sigma $$</EquationSource> </InlineEquation>-algebras

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 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\sigma $$</EquationSource> </InlineEquation>-algebra. We show that, for countably generated <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\sigma $$</EquationSource> </InlineEquation>-algebras, the larger it is, the larger the information is. The same is true for general <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$\sigma $$</EquationSource> </InlineEquation>-algebras after the removal of a negligible set of states. Copyright Springer-Verlag Berlin Heidelberg 2013