Radon-Nikodym导数的可计算性

IF 0.2

De Computis-Revista Espanola de Historia de la Contabilidad Pub Date : 2011-06-27 DOI:10.3233/COM-2012-005

M. Hoyrup, Cristobal Rojas, K. Weihrauch

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引用次数: 37

摘要

我们证明了单次应用不可计算算子EC，将集合(N)的枚举变换为它们的特征函数，就足以计算绝对连续σ-有限测度λ的Radon-Nikodym导数dµ/dλ。我们还给出了这两个测度的一个条件(从涉及这两个测度的某线性算子的范数的可计算性来看)，该条件足以计算导数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Computability of the Radon-Nikodym Derivative

We show that a single application of the noncomputable operator EC, which transforms enumerations of sets (in N) to their characteristic functions, suffices to compute the Radon-Nikodym derivative dµ/dλ of a finite measure µ, which is absolutely continuous w.r.t. the σ-finite measure λ. We also give a condition on the two measures (in terms of computability of the norm of a certain linear operator involving the two measures) which is sufficient to compute the derivative.

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来源期刊

De Computis-Revista Espanola de Historia de la Contabilidad BUSINESS, FINANCE-

自引率

50.00%

发文量