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ISSN : 1226-0657

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Vol.6 No.1
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A NOTE ON THE INTEGRATION WITH RESPECT TO FINITELY ADDITIVE SET FUNCTIONS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1999, v.6 no.1, pp.17-25
Kim, Bong-Jin (Department of Mathematics, Daejin University)
Kim, Bong-Jin. (1999). A NOTE ON THE INTEGRATION WITH RESPECT TO FINITELY ADDITIVE SET FUNCTIONS. 한국수학교육학회지시리즈B:순수및응용수학, 6(1), 17-25.
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Abstract

In this paper, we investigate the properties of the Dunford-Schwartz integral (the integral with respect to a finitely additive measure). Though it is not equivalent to the cylinder integral, we can show that a cylinder probability v on (H, C) can be extend as a finitely additive probability measure <TEX>$\hat{v}$</TEX> on a field <TEX>$\hat{C}{\;}{\supset}{\;}C$</TEX> which is equivalent to the Dunford-Schwartz integral on (<TEX>$H,{\;}\hat{C},{\;}\hat{v}$</TEX>).

keywords
cylinder probability, cylinder integral, finitely additive set function, Dunford-Schwartz integral

한국수학교육학회지시리즈B:순수및응용수학

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