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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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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: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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. , 6(1), 17-25.

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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