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1996/1997 A characterization theorem for the existence of a Hellinger-type integral
William D. L. Appling
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Real Anal. Exchange 22(1): 236-264 (1996/1997).


Suppose that \(a \lt b\) and each of \(h\) and \(m\) is a real-valued function defined on \([a;b]\) with \(m\) nondecreasing such that if \([p;q]\subseteq [a;b]\) and \(m\vert_p^q = 0\), then \(h\vert_p^q = 0\). There are developed, among other things, necessary and sufficient conditions in order that for each real-valued function \(f\) defined and quasi-continuous on \([a;b]\), the Hellinger-type integral \[\int_{[a;b]}{{dfdh}\over {dm}}\] exists. As is well known, this integral has arisen in connection with, among other things, representation theorems for certain classes of continuous linear functionals.


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William D. L. Appling. "A characterization theorem for the existence of a Hellinger-type integral." Real Anal. Exchange 22 (1) 236 - 264, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 1 June 2012

zbMATH: 0879.28007
MathSciNet: MR1433611

Primary: 28A25

Keywords: bounded difference quotient variation , convex decomposition , integral existence characterization

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 1 • 1996/1997
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