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Feynman's formulae for products. $$\iiint\limits_{[0,1]^3}\frac{x_1^2 x_2}{[(a_4-a_3)x_3 x_2x_1+(a_3-a_2)x_2 x_1+ (a_2-a_1)x_1+a_1]^4}dx_1dx_2dx_3=$$ $$=\int\limits_{0}^{1}dx_1\int\limits_{0}^{1-x_1}d …

This is one of my all time favourites (quoted from Problems and Theorems in Analysis by Polya and Szego). The 3D domain $\mathcal D$ is defined by the inequalities $$-1\leq x,y,z\leq 1,\quad -\ …

This is impossible. Baire proved that if a function defined on $\mathbb R$ is of Baire class 1, then it is continuous everywhere except, possibly, for a meagre set. And by another Baire's theorem a co …

To add a bit to Jonas Meyer's answer. Sierpiński's result was first published in C.R. Soc. Sc. Varsovie 1928, p. 84-87. It was reproduced in his monograph "Hypothèse du continu" (Lwów, 1934, p. 52): …

This is true. By a partition of unity, the proof can be reduced to the case when the test functions have their supports in a unit cube and the result follows from a more or or less straightforward …

There is a bunch of such statements which can be obtained by Stein's method. You might be interested in the paper "On the Rate of Convergence in the Multivariate CLT" by Gotze, which is specifically …

L'Hôpital's rule was first published in Analyse des Infiniment Petits. According to The Historical Development of The Calculus by Edwards (p. 269), L'Hospital's argument, which is stated verbally w …

Let $E$ and $E'$ be Banach spaces. Mappings $f:E\to E'$, which satisfy the inequality $$\|f(x + y) − f(x) − f(y)\| \leq\epsilon$$ for all $x, y \in E$, are called $\epsilon$-additive (or approximate …