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Have you ever encountered a scenario where interchanging limit with integral in practice was not allowed?

Go McGill :))

Also when you talk about the divergence theorem using Lebesuge integration, you're tending into the territory of Geometric Measure Theory which is very deep and im not sure why any…

This is an amazing book and I'm so suprised to see someone else knows about it. However , who cares about the Lebesgue integral? The only thing its good for is integrating patholog…