Real Analysis Exchange

Strong convergence in Henstock-Kurzweil-Pettis integration under an extreme point condition.

B. Satco

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In the present paper, some Olech and Visintin-type results are obtained in Henstock-Kurzweil-Pettis integration. More precisely, under extreme or denting point condition, one can pass from weak convergence (i.e. convergence with respect to the topology induced by the tensor product of the space of real functions of bounded variation and the topological dual of the initial Banach space) or from the convergence of integrals to strong convergence (i.e. in the topology of Alexiewicz norm or, even more, of Pettis norm). Our results extend the results already known in the Bochner and Pettis integrability setting.

Article information

Real Anal. Exchange, Volume 31, Number 1 (2005), 179-194.

First available in Project Euclid: 5 June 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 28B20: Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14] 26A39: Denjoy and Perron integrals, other special integrals 46B20: Geometry and structure of normed linear spaces

Keywords: Henstock-Kurzweil-Pettis integral extreme point denting point


Satco, B. Strong convergence in Henstock-Kurzweil-Pettis integration under an extreme point condition. Real Anal. Exchange 31 (2005), no. 1, 179--194.

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