C-DUNFORD INTEGRAL AND C-PETTIS INTEGRAL

Abstract

In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and CPettis integral. We prove that a function f is C-Dunford integrable if and only if x∗f is C-integrable for each x∗ ∈ X ∗ and prove the controlled convergence theorem for the C-Pettis integral.

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