Information and \sigma -algebras |
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Authors: | Carlos Hervés-Beloso Paulo Klinger Monteiro |
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Institution: | 1. RGEA, Facultad de Económicas, Universidad de Vigo, Vigo, Spain 2. FGV/EPGE, Praia de Botafogo 190/1103, Rio de Janeiro RJ, Brazil
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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 $\sigma $ -algebra. We show that, for countably generated $\sigma $ -algebras, the larger it is, the larger the information is. The same is true for general $\sigma $ -algebras after the removal of a negligible set of states. |
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