Abstract
A natural and general way to model information in a microeconomic system is to specify it as a sub-σ-field (of the σ-field of events, or measurable subsets of the set of states of the world). Several apparently different definitions of convergence have been introduced. For continuous time trading models, relationships between continuous information (assumed to be increasing and right continuous) and various continuity properties of asset prices have been studied by Harrison and Huang. For a static general equilibrium pure exchange economy, the information topology advocated by Allen yields continuity of microeconomic behavior (i.e., continuous dependence of agents’ demand functions on their state dependent utilities, initial endowments, and information) and of the value of information. Additional convergence notions for σ-fields appear in the probability theory literature. This paper compares these convergence notions and analyzes when it can be said that one is weaker than another.
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© 1984 Springer-Verlag Berlin Heidelberg
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Allen, B. (1984). Convergence of σ-Fields and Applications to Mathematical Economics. In: Hammer, G., Pallaschke, D. (eds) Selected Topics in Operations Research and Mathematical Economics. Lecture Notes in Economics and Mathematical Systems, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45567-4_11
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DOI: https://doi.org/10.1007/978-3-642-45567-4_11
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