A characterization of internal sets
A completeness theorem for two-parameter stochastic processes
A Daniell integral approach to nonstandard Kurzweil-Henstock integral
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
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 -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 general theory of superinfinitesimals
A Hamiltonian property of connected sets in the alternative set theory.
A Loeb Measure Approach To The Riesz Representation Theorem
A new proof of Kelley's Theorem
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.
A nonstandard approach to fuzzy set theory
A non-standard approach to the Euclidean study of plane curves.
A nonstandard treatment with quantities
A sequential approach to a construction of measures
A walk through nonstandard analysis on the paths of A. Robinson. (Balade en analyse non standard sur les traces de A. Robinson.)
An application of nonstandard analysis to functional equations.
An elimination of infinitely small quantities and infinitely large numbers (within the framework of AST)
An elimination of the predicate “to be a standard member” in nonstandard models of arithmetic
Analyse relative
Approximation diophantienne et distances ultramétriques non standard
Asymptotique dans un corps de Hardy
Biequivalence vector spaces in the alternative set theory
As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field of all rational numbers) are introduced and their basic properties are listed. A methodological consequence opening a new view towards the relationship between the algebraic and topological dual is quoted. The existence of various types of valuations on a biequivalence vector space inducing its biequivalence is proved. Normability is characterized in terms of total...