# Tagged Questions

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### Correspondence as a graph of a multifunction

Suppose I'd like to say that a projection of $R\subset X\times Y$ on $X$ is the whole $X$. That is, $R$ is a graph of a certain multifunction, or equivalently it is a left-total relation. I do ...
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### How to show $\mathcal{B}(\mathbb{R}^2)=\mathcal{B}(\mathbb{R})\otimes\mathcal{B}(\mathbb{R})$?

I would like to show that $$\mathcal{B}(\mathbb{R}^2) = \mathcal{B}(\mathbb{R})\otimes\mathcal{B}(\mathbb{R}).$$ Can you say me what is a good way to show that? My idea is to show it via generators ...
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### Measure and empty set second version

If A is a nonempty open set, the measure of A is not 0 ...first open set is uncountable, I pick up one interval irrational intersect [ 0,1 ] with measure 1 ...however this is not open...I am wondering ...
### Elementary measure theory exercise about $\liminf_{n \to \infty} \mu (E_n)$ [duplicate]
I'm going through the Fremlin's book (vol 1) on my own, and frankly, I don't have any good idea where to begin with the following exercise: Assuming that ($X, \Sigma, \mu$) is an measure space and ...