The definition and properties of an abstract and very general nonparametric integral of the calculus of variations are proposed. We obtain some existence theorems, a Tonelli type theorem and consequently a representation results in terms of a Lebesgue-Stieltjes integral. A suitable convergence theorem for martingales is the main tool of this last result.
The non-parametric integral of the calculus of variations as a Weierstrass integral. I. Existence and representation
BRANDI, Primo;SALVADORI, Anna
1985
Abstract
The definition and properties of an abstract and very general nonparametric integral of the calculus of variations are proposed. We obtain some existence theorems, a Tonelli type theorem and consequently a representation results in terms of a Lebesgue-Stieltjes integral. A suitable convergence theorem for martingales is the main tool of this last result.File in questo prodotto:
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