THE HENSTOCK-PETTIS INTEGRAL OF BANACH SPACE-VALUED FUNCTIONS

  • Park, Jae Myung (Department of Mathematics Chungnam National University) ;
  • Lim, Jong Tae (Department of Mathematics Chungnam National University) ;
  • Kim, Young Kuk (Department of Mathematics Education Seowon University)
  • Received : 2006.06.30
  • Published : 2006.09.30

Abstract

In this paper, we study the Henstock-Pettis integral of Banach space-valued functions mapping an interval [0, 1] in R into a Banach space X. In particular, we show that a Henstock integrable function on [0, 1] is Henstock-Pettis integrable on [0, 1] and a Pettis integrable function is Henstock-Pettis integrable on [0, 1].

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