Nonlinear integration on Lp-spaces |
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| Authors: | Richard A Alò André de Korvin Vo Van Tho |
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| Institution: | 1. Department of Mathematics, Lamar University, Beaumont, Texas 77706, USA;2. Indiana State University, Terre Haute, Indiana 47809 USA |
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| Abstract: | For a Banach space E and for 1 ? p < ∞ let ?p<∞ let LEp(μ) = LEp(S,B,μ) denote all Bochner p-integrable E-valued functions on a measure space (S,B,μ). Under study are convergence theorems for integrals of functions in LEp(μ) with respect to Nemytskii measures. Weak integrals are then denoted to Hammerstein operators, and a study of topologies generated by vector measures leads to a characterization of compact Hammerstein operators. |
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