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A Daniell integral approach to nonstandard Kurzweil-Henstock integral

Ricardo Bianconi, João C. Prandini, Cláudio Possani (1999)

Czechoslovak Mathematical Journal

A workable nonstandard definition of the Kurzweil-Henstock integral is given via a Daniell integral approach. This allows us to study the HL class of functions from . The theory is recovered together with a few new results.

A new proof of Kelley's Theorem

S. Ng (1991)

Fundamenta Mathematicae

Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.

Analyse relative

Yves Peraire (1992)

Annales scientifiques de l'Université de Clermont. Mathématiques

Asymptotic Solutions of nonlinear difference equations

I. P. van den Berg (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We study the asymptotics of first-order nonlinear difference equations. In particular we present an asymptotic functional equation for potential asymptotic behaviour, and a theorem stating sufficient conditions for the existence of an actual solution with such asymptotic behaviour.

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