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$%G. Vera, Pointwise compactness and continuity of the integral, Rev. Mat. Univ. Complut. Madrid 9 (1996), supplementary, 221–245.%$

In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in spaces endowed with the topology of pointwise convergence on a dense subset in .

1991 Mathematics Subject Classification: 28A40, 46A50, 28B05, 46B26, 28-02.