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- W2019435325 abstract "We present a theory of measure and integration in topological vector spaces and generalize the Fichtenholz-Kantorovich-Hildebrandt and Riesz representation theorems to this setting, using strong integrals. As an application, we find the containing Banach space of the space of continuous $p$-normed space-valued functions. It is known that Bochner integration in $p$-normed spaces, using Lebesgue measure, is not well behaved and several authors have developed integration theories for restricted classes of functions. We find conditions under which scalar measures do give well-behaved vector integrals and give a method for constructing examples." @default.
- W2019435325 created "2016-06-24" @default.
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- W2019435325 date "1972-01-01" @default.
- W2019435325 modified "2023-10-18" @default.
- W2019435325 title "Integral representation theorems in topological vector spaces" @default.
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- W2019435325 doi "https://doi.org/10.1090/s0002-9947-1972-0312264-0" @default.
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