Abstract
The points of Gateaux and Fréchet differentiability in L∞(μ, X) are obtained, where (Ω, ∑, μ) is a finite measure space and X is a real Banach space. An application of these results is given to the space B(L1(μ, ℝ), X) of all bounded linear operators from L1(μ, ℝ) into X.
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