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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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Recovering measure from the family of sigma-subalgebras
Let $(X,\mathscr{F})$ be a measurable space.
Let $\mathscr{F}_\alpha \subseteq \mathscr{F}$, $\alpha \in \mathfrak{A}$ be a class of $\sigma$-subalgebras.
Let we have a measure $\mu_\alpha$ on every …