A measure on $\mathcal{B}_2$ is called a two dimensional Borel measure. Suppose that $\mu$ and $\nu$ are finite two dimensional Borel measures such that $\mu(A\times B) = \nu(A \times B)$ for all $A,B\in \mathcal{B}$. Prove that $\mu = \nu$. Is this just a uniqueness proof? I ran into this in the book I am using, but I'm not sure what to do here. Can anyone give me a hint on it?
2026-03-25 19:17:34.1774466254
Two dimensional Borel Measure proof
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