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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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Measurable multifunction

Let $f:[a,b]\times \mathbb{R}^{n} \times \mathbb{R}^{m} \rightarrow \mathbb{R}^{n}$. Suppose $ f (.,x, u) $ is Lebesgue measurable for each $(x,u)$. Suppose also that $ f $ is continuous at $ (x, u) $ …