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I'm exploring differentiation under the integral sign (I want to be much faster and more assured in doing this common task). So one thing I'm interested in is good counterexamples, where both ...

Consider a measurable radial function $u:\Bbb R^d\to(0,\infty)$ such that $$\int_{B_\delta(0)} u(x) d x=\infty\quad\forall\,\, \delta>0.$$ I would like to prove or to disprove that there exists $r&...

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 ...

A first stab at a definition of surface area might go like this: Let S be a surface. Select finitely many points from S and make a bunch of triangles having these points as vertexes. Add up the ...