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- W2048653935 abstract "The classic definition of line integral of one-forms does not apply when the line is not smooth. In this article it is analyzed from the point of view of measure theory, the problem of approximating a line integral using the quotient of Newton instead of the derivative. The expected value of a certain scheme of approximation of line integrals of closed one-forms, with respect to the Wiener measure, is computed. In particular, if a form is harmonic, then the expected value of the line integral is Zero. La définition classique de l'intégrale de ligne des un-formes ne s'applique pas quand la ligne n'est pas lisse. En cet article elle est analysée du point de vue de la théorie de mesure, le probleme de rapprocher une intégrale de ligne en utilisant le quotient de Newton au lieu du dérivé. La valeur prévue d'un certain arrangement d'approximation des intégrales de ligne des un-formes fermées, en ce qui concerne la mesure de Wiener, est calculée. En particulier, si une forme est harmonique, alors la valeur prévue de l'intégrale de ligne est zéro." @default.
- W2048653935 created "2016-06-24" @default.
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- W2048653935 date "2007-01-01" @default.
- W2048653935 modified "2023-10-02" @default.
- W2048653935 title "The expected value of the line integral of one-forms" @default.
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- W2048653935 doi "https://doi.org/10.1016/j.bulsci.2006.03.007" @default.
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