Solution to the integrated Cauchy functional equation on the whole line

Lau, Ka-Sing ; Rao, C. R. (1984) Solution to the integrated Cauchy functional equation on the whole line Sankhya, 46 (3). pp. 311-318. ISSN 0972-7671

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Abstract

A general solution of the integrated Cauchy functional equation ∫-f(x+y)dμ(y)=f(x)a.e. for x6(-∞,∞) is obtained under the only restriction that f is a locally integrable positive function and μ is a σ-finite positive Borel measure on R. This problem can be solved by an application of a general theorem due to Deny based on Choquet theory. However, we provide an alternative approach to the problem by using the more familiar Krein-Milman theorem.

Item Type:Article
Source:Copyright of this article belongs to Indian Statistical Institute.
Keywords:Choquet-Deny Theorem; Deny Theorem; Integrated Cauchy Functional Equation; Krein-Milman Theorem
ID Code:96511
Deposited On:10 Jan 2013 10:52
Last Modified:10 Jan 2013 10:52

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