THE MEASURE-THEORETIC ASPECTS OF ENTROPY .1.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:40

Article

MASANI, PR

关键词: ENTROPY;    INFORMATION;    MEASURE;    PROBABILITY;   

DOI  :  10.1016/0377-0427(92)90107-9

来源: Elsevier

【 摘 要 】

Let P be a countably additive probability measure and mu be any [0,infinity]-valued countably additive measure, both on a sigma-algebra A over a space OMEGA. We define a (P-, mu-dependent) countably additive measure H on the delta-ring A(mu) = (A: A is-an-element-of A and mu(A) < infinity) with values in (-infinity, +infinity] with the property that in case OMEGA is-an-element-of A(mu), H(OMEGA) is the total entropy of P relative to mu. We study the Lebesque decomposition of H with respect to mu.

【 授权许可】

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