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Gauge integrals and series

Charles W. Swartz (2004)

Mathematica Bohemica

This note contains a simple example which does clearly indicate the differences in the Henstock-Kurzweil, McShane and strong McShane integrals for Banach space valued functions.

Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation

Nikolay Tzvetkov, Nicola Visciglia (2013)

Annales scientifiques de l'École Normale Supérieure

Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.

General multifractal analysis of local entropies

Floris Takens, Evgeny Verbitski (2000)

Fundamenta Mathematicae

We address the problem of the multifractal analysis of local entropies for arbitrary invariant measures. We obtain an upper estimate on the multifractal spectrum of local entropies, which is similar to the estimate for local dimensions. We show that in the case of Gibbs measures the above estimate becomes an exact equality. In this case the multifractal spectrum of local entropies is a smooth concave function. We discuss possible singularities in the multifractal spectrum and their relation to phase...

General theory of the fuzzy integral.

Pietro Benvenuti, Doretta Vivona (1996)

Mathware and Soft Computing

By means of two general operations + and x, called pan-operations'', we build a new kind of integral. This formulation contains, as particular cases, both Choquet's and Sugeno's integrals.

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