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Journal of the London Mathematical Society 1985 s2-32(3):479-487; doi:10.1112/jlms/s2-32.3.479
© 1985 by London Mathematical Society
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© Oxford University Press

Pettis Integrability of Weakly Continuous Functions and Baire Measures

A. J. Pallarés and G. Vera

Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Murcia 30001 Murcia, Spain

We analyse the Pettis integrability of weakly continuous bounded functions defined on a completely regular space S and taking values in a Banach space. We prove that the set of Baire measures with respect to which such functions are universally Pettis integrable is precisely the space Mg(S) of Grothendieck measures introduced by Wheeler. This leads us to prove that Mg(S) is {sigma}(Mg(S), Cb(S))-sequentially complete, and we obtain a characterization in rß(S) of the measures in Mg(S). We also obtain analogous results for the space of separable measures M{infty}(S).


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