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Let $G$ be a topological group and $\mathcal{B}$ its Baire $\sigma$-algebra (i.e. the smallest $\sigma$-algebra for which all continuous functions $G\rightarrow\mathbb{R}$ are measurable). Consider the product map $\cdot :G\times G\rightarrow G$ given by $(g,h)\mapsto g \cdot h$. Question: Is the...