Let $B_k$ be the sigma-algebra of all Borel sets in $\mathbb R^k$. How can we prove that $B_{m+n}=B_m * B_n$? I am a beginner in analysis, hope to seek help here.
Prove $B_{m+n}=B_m * B_n$ if $B_k$ is the sigma-algebra of all Borel sets in $\mathbb R^k$
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banach-spaces