On Denjoy-Dunford and Denjoy-Pettis integrals

José L.  Gámez; José Mendoza

ArticleOriginal scientific text

Title

On Denjoy-Dunford and Denjoy-Pettis integrals

Authors ¹, ¹

Affiliations

Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain.

Abstract

The two main results of this paper are the following: (a) If X is a Banach space and f : [a,b] → X is a function such that x*f is Denjoy integrable for all x* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function

f : [a, b] \to c_{0}

which is not Pettis integrable on any subinterval in [a,b], while

ʃ_{J} f

belongs to

c_{0}

for every subinterval J in [a,b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dundord and Denjoy-Pettis integrals are studied.

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Title

On Denjoy-Dunford and Denjoy-Pettis integrals

Affiliations

Abstract

Bibliography