# Tagged Questions

Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...

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### Reference for a proof of the fiberwise Stokes theorem

The fiberwise Stokes theorem says that given a differential form on a smooth fiber bundle whose fibers have boundary, the difference between the fiberwise integral of the differential and the ...
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### Minkowski's Inequality for Integrals in Orlicz spaces

EDIT: I have changed the question to have less parameters, fitting it into the context of Orlicz spaces. Suppose $f:[0,\infty)\to[0,\infty)$ is convex and increasing, $f^{-1}:[0,\infty)\to[0,\infty)$...
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Suppose that $f$ is $1$-periodic and that $f \in {L^{p}}([0,1)$, where $p > 1$. Let $$(D_{n})_{n \in \mathbb{N}_{0}} = \left( \left\{ I^{n}_{j},~ 1\leq j \leq 2^{n} \} \right\} \right)_{n ... 0answers 111 views ### motivic integration and jacobian ideal When we consider the change of variables in motivic integration, we have a birational map f:Y\rightarrow X with Y smooth and we have to consider two invariants the order of the Jacobian ideal of X ... 0answers 107 views ### What are the criteria for an elementary function to be infinitely integrable in elementary functions? What features of elementary functions define a class of functions whose consecutive indefinite integration also gives an elementary function? Is there a way to check whether a given elementary ... 0answers 239 views ### When does this method for integrals of fractional/integer parts work? In a question Agno suggested an interesting way to compute \{x\} and \zeta(s). Define$$ F(x) = \{x\} = x - \lfloor x \rfloor = \frac{i \, \log\left(-e^{\left(-2 i \, \pi x\right)}\right)}{2 \, \...
Hello, The Hubbard-Stratonovich transformation $\exp(x^2) = \frac{1}{\sqrt{4 \pi}} \int_{-\infty}^{+\infty} du \exp(-\frac{u^2}{4} - xu)$ allows one to wirte the exponential of a the square of a ...