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Théorème: Quelle que soit une fonction f(x) à carré sommable qu'on suppose définie aux points de l'intervalle (0,1) et nulle ailleurs, l'intégrale q(x) = ∫_0^1 (f(x+α)-f(x-α))/α dα considérée comme lim_{ϵ=0}∫_{ϵ}^1, est finie presque partout dans (0,1) et représente une fonction de x à carré sommable. Le but de cette note est de trouver une limite supérieure pour l'intégrale ∫_0^1[q(x)]^2dx, et de donner une démonstration du théoreme cité, en se servant d'une méthode des variables réelles qui permet...
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