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- W2167839048 abstract "There are several generalizations of the space L1(R) of Lebesgue integrable functions taking values in the real numbers R (and defined on the usual Lebesgue measure space (Ω,Σ, μ) on [0, 1] ) to a space of strongly-measurable “integrable” (suitably formulated) functions taking values in a Banach space X. The most common generalization is the space L1(X) of Bochner-Lebesgue integrable functions. Using the fact [P1, Theorem 1.1] that a strongly-measurable function is essentially separably-valued, one can easily extend Lebesgue’s Differentiation Theorem from L1(R) to L1(X). Specifically [B; cf. DU, Theorem II.2.9], if f ∈ L1(X), then lim h→0 1 h ∫ t+h" @default.
- W2167839048 created "2016-06-24" @default.
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- W2167839048 date "2009-01-01" @default.
- W2167839048 modified "2023-09-22" @default.
- W2167839048 title "AN APPLICATION OF A PISIER FACTORIZATION THEOREM TO THE PETTIS INTEGRAL" @default.
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