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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 general approach to decomposable bi-capacities

Susanne Saminger, Radko Mesiar (2003)

Kybernetika

We propose a concept of decomposable bi-capacities based on an analogous property of decomposable capacities, namely the valuation property. We will show that our approach extends the already existing concepts of decomposable bi-capacities. We briefly discuss additive and $k$ -additive bi-capacities based on our definition of decomposability. Finally we provide examples of decomposable bi-capacities in our sense in order to show how they can be constructed.

A Nonstandard Approach to the Uniqueness Problem for the Navier-Stokes Equations.

M. Capinski, N.J. Cutland (1994)

Monatshefte für Mathematik

A notion of measure for classes in AST

Athanossios Tzouvaras (1987)

Commentationes Mathematicae Universitatis Carolinae

A sequential approach to a construction of measures

Martin Kalina (1989)

Commentationes Mathematicae Universitatis Carolinae

A walk through nonstandard analysis on the paths of A. Robinson. (Balade en analyse non standard sur les traces de A. Robinson.)

Pétry, André (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

Alternative definitions of conditional possibilistic measures

Ivan Kramosil (1998)

Kybernetika

The aim of this paper is to survey and discuss, very briefly, some ways how to introduce, within the framework of possibilistic measures, a notion analogous to that of conditional probability measure in probability theory. The adjective “analogous” in the last sentence is to mean that the conditional possibilistic measures should play the role of a mathematical tool to actualize one’s degrees of beliefs expressed by an a priori possibilistic measure, having obtained some further information concerning...

An expression of classical dynamics

J.-J. Moreau (1989)

Annales de l'I.H.P. Analyse non linéaire

Automorphisms of the Loeb algebra

David Ross (1987)

Fundamenta Mathematicae

Borel classes in AST. Measurability, cuts and equivalence

Martin Kalina, Pavol Zlatoš (1989)

Commentationes Mathematicae Universitatis Carolinae

Choquet-like integrals with respect to level-dependent capacities and $ϕ$ -ordinal sums of aggregation function

Radko Mesiar, Peter Smrek (2015)

Kybernetika

In this study we merge the concepts of Choquet-like integrals and the Choquet integral with respect to level dependent capacities. For finite spaces and piece-wise constant level-dependent capacities our approach can be represented as a $ϕ$ -ordinal sum of Choquet-like integrals acting on subdomains of the considered scale, and thus it can be regarded as extension method. The approach is illustrated by several examples.

Convergence in incomplete market models.

Kopp, P.Ekkehard, Wellmann, Volker (2000)

Electronic Journal of Probability [electronic only]

Correction to the paper “A notion of measure for classes in AST”

Athanossios Tzouvaras (1988)

Commentationes Mathematicae Universitatis Carolinae

Dominated and uniformly dominated families of Loeb-measures.

Dieter Landers, Lothar Rogge (1988)

Mathematica Scandinavica

Finitely-additive, countably-additive and internal probability measures

Haosui Duanmu, William Weiss (2018)

Commentationes Mathematicae Universitatis Carolinae

We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is infinitesimal. As an application to standard probability theory, we show that every finitely-additive Borel probability measure $P$ on a separable metric space is a limit of a sequence of countably-additive Borel probability measures ${P_{n}}_{n \in ℕ}$ in the sense that $\int f d P = {lim}_{n \to \infty} \int f d P_{n}$ for all bounded...

Fonctions Généralisées et Analyse Non Standard.

Antoine Delcroix (1997)

Monatshefte für Mathematik

Loeb completion of internal vector-valued measures.

Rade T. Zivaljevic (1985)

Mathematica Scandinavica

Nearstandardness on a finite set [Book]

Lyantse V. (1997)

Nonstandard Integration Theory in Topological Vector Lattices.

Peter A. Loeb, Horst Osswald (1997)

Monatshefte für Mathematik

Nonstandard methods for Navier-Stokes equations

Nigel J. Cutland, Marek Capinski (1993)

Revista colombiana de matematicas

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