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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Notes
Rohlin appears in A.M.S. Translation (71). Later, it is written Rohklin.
Without loss of generality, we may take \(C=\mathbb R \).
Please excuse us for not repeating Dubra and Echenique’s calculations.
We owe this observation to Greinecker and Dubra.
A Lusin space is a pair \(\left( \varOmega ,\fancyscript{B}\right) \) where \(\varOmega \) is analytic and \(\fancyscript{B}\) is the Boreleans \(\sigma \)-algebra.
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We thank the comments from the participants at Naples II Workshop on Equilibrium Analysis Under Ambiguity, 2011, SAET-2011 and Exeter workshop in honor of Cuong Le Van, 2011. In particular, we gratefully acknowledge the comments of A. Citanna, B. Cornet, J. Dubra, F. Echenique, M. Grandmont, M. Greinecker, F. Maccheroni, J.P. Torres-Martínez and N. Yannelis. We also acknowledge the referee for various suggestions and some references. Carlos thanks the partial support of Research Grants ECO2009-14457-C04-01 (Ministerio de Ciencia e Innovación) and 10PXIB300141PR, RGEA (Xunta de Galicia and FEDER). Paulo acknowledges the financial support of CNPq, Brazil.
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Hervés-Beloso, C., Monteiro, P.K. Information and \(\sigma \)-algebras. Econ Theory 54, 405–418 (2013). https://doi.org/10.1007/s00199-012-0723-1
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DOI: https://doi.org/10.1007/s00199-012-0723-1