Relative Entropy as a Countably-Additive Measure

P. R. Masani
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P. R. Masani: University of Pittsburgh, Department of Mathematics and Statistics

A chapter in Stochastic Processes, 1993, pp 263-274 from Springer

Abstract: Abstract Let P be a countably additive probability measure, and μ be any countably additive [0, ∞]-valued measure, both on a σ-algebra A over a space Ω. We define a (P, μ dependent) countable additive measure H on the δ-ring A μ of sets A ∈ A such that μ(A) A μ , H(Ω) is the total entropy of P relative to μ. We study the extension of H beyond A μ, and its Lebesgue decomposition with respect to μ.

Keywords: Relative Entropy; Total Entropy; Entropy Measure; Cardinality Measure; Countably Additive (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-7909-0_29

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DOI: 10.1007/978-1-4615-7909-0_29

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