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D'après le théorème connu du Lebesgue-Fubini si la fonction f(x,y) de deux variables x,y est sommable dans le rectangle P=(a,b;c,d), c'est-à-dire, s'il existe l'intégrale double finie ∫_{P}f(x,y)dxdy (1) (au sens de Lebesgue), on a constamment ∫_{F}dy∫_{E}f(x,y)dx =∫_{E}dx∫_{F}f(x,y)dy (2) pourvu que les ensembles mesurables E et F soient compris respectivement dans les intervalles (a,b) et (c,d). D'autre part, si la fonction f(x,y) est mesurable superficiellement et de signe constant, il suffit...
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