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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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Make this marginalization statement rigorous

Intuition tells me that $$ p(x\,|\,y) = \int p(x,\theta\,|\,y) \; d\theta$$ by the "law of marginalization", pretty much for any object $\theta$. I would like to make this statement rigorous, however. …
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