integral representation of linear functionals on spaces of sections
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PROCEEDINGS OF THE AMERICAN MATHEMATICAL Volume
91, Number
4, August
SOCIETY 1984
INTEGRAL REPRESENTATION OF LINEAR FUNCTIONALS ON SPACES OF SECTIONS ANTHONY KAREL SEDA ABSTRACT. An integral representation is given of functionals on the normed linear space of all sections, with compact support, of a Banach bundle p: E —* X. This representation is shown to be equivalent in a certain sense to the strong lifting property on X and to the disintegration of measures property on spaces q : Y —>X over X.
1. Introduction. In the appendix of [5], see Problems B and C there, Gierz and Keimel study the following question. Given a Banach bundle p: E —*X over a compact Hausdorff space X, and a bounded linear functional defined on the Banach space T(p) of all sections of p, find functionals r¡x G E* with ||r;x|| < 1 for each x G X and a measure p cm X such that (
