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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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the intersection of a sequence of measurable sets

If $\Omega$ is a bounded open set in $R^n$, $\Omega_j\subset\Omega$, and $|\Omega_j|\geq\epsilon$, which $\epsilon$ is a constant. Can we say there is a subsequence $\Omega_{j_k}$ of $\Omega_j$, such …