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Let be $X$ a metric compact space and $(G,+)$ a topological compact abelian group. Let be $\mathcal{A}$ the Borel $\sigma$-algebra of $X$ and $\mathcal{B}$ the Borel $\sigma$-algebra of $G$. Consider in $X\times G$ the product $\sigma$-algebra.

My Question: I have a Borelian $A\times G$ of $X\times G.$ I want to show is that the set $ A $ must be necessarily a borel set of $X$

  • 1
    If the set $A\times G$ is a rectangle, $A$ must be a [measurable section](http://unapologetic.wordpress.com/2010/07/19/sections-of-sets-and-functions/).2012-10-12
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    If $A \times G$ is a rectangle then it is obvious that A is a borel set.2012-10-12
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    Otherwise, the set will nly be analytic, not Borel.2012-10-12

4 Answers 4