## Real Analysis Exchange

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

B. Satco

#### Abstract

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

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

Dates
First available in Project Euclid: 5 June 2006

https://projecteuclid.org/euclid.rae/1149516809

Mathematical Reviews number (MathSciNet)
MR2218197

Zentralblatt MATH identifier
1111.28009

#### Citation

Satco, B. Strong convergence in Henstock-Kurzweil-Pettis integration under an extreme point condition. Real Anal. Exchange 31 (2005), no. 1, 179--194. https://projecteuclid.org/euclid.rae/1149516809

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