Czechoslovak Mathematical Journal, Vol. 69, No. 1, pp. 45-53, 2019
A remark on weak McShane integral
Kazushi Yoshitomi
Received March 31, 2017. Published online August 6, 2018.
Abstract: We characterize the weak McShane integrability of a vector-valued function on a finite Radon measure space by means of only finite McShane partitions. We also obtain a similar characterization for the Fremlin generalized McShane integral.
Keywords: weak McShane integral; finite McShane partition; Radon measure space
Affiliations: Kazushi Yoshitomi, Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Minamiohsawa 1-1, Hachioji, Tokyo 192-0397, Japan, e-mail: yositomi@tmu.ac.jp