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The following problem is a stumbling block in a research project that I am working on: Problem. Let $ G $ be a second-countable locally compact Hausdorff group with a fixed Haar measure. Is it tru …

I spent some time searching MathOverflow for a problem that would resemble the one given below, but it turned out to be a rather futile endeavor. I was led to this problem in my attempts to construct …

Let $ (X,\Sigma,\mu) $ be a measure space and $ B $ a Banach space. According to my understanding, a function $ f: X \to B $ is said to be strongly $ \mu $-measurable if and only if it is the almost-e …

Let $ G $ be a second-countable, locally compact Hausdorff group and $ B $ a separable Banach space. We say that a function $ f: G \to B $ is Bochner-measurable if and only if it is the everywhere po …

Let $ (X,\Sigma,\mu) $ be a $ \sigma $-finite measure space and $ B $ a Banach space. A function $ f: X \to B $ is said to be strongly $ \mu $-measurable iff it is the almost-everywhere pointwise limi …

This question is related to something that I asked yesterday: If $ F(x,\bullet) \in {L^{\infty}}(G,B) $ for all $ x \in G $, then is $ x \mapsto F(x,\bullet) $ strongly measurable? Pietro Majer provi …

This question is related to another one that I asked two days ago. Question. Does there exist a Borel subset $ M $ of $ \mathbb{R}^{2} $ with the following two properties? The projecti …