Convergence theorems for set-valued Denjoy-Pettis integrable mappings

Chun-Kee Park

doi:10.4134/CKMS.2009.24.2.227

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Commun. Korean Math. Soc. 2009; 24(2): 227-237

Printed June 1, 2009

https://doi.org/10.4134/CKMS.2009.24.2.227

Convergence theorems for set-valued Denjoy-Pettis integrable mappings

Chun-Kee Park

Kangwon National University

Abstract

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Abstract

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued Denjoy-Pettis integrable mappings.

Keywords: set-valued mapping, Denjoy integral, Denjoy-Pettis integral

MSC numbers: 26A39, 28B05, 28B20