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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

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Bochner measurable; continuous operator

Can you specify which $\sigma$-algebra and measure you have on $\Omega$? Bochner measurability is defined as being the limit a.e. of measurable finitely valued functions. By Pettis' Theorem this is th …
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