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 hereditary property of HM-spaces.
A hypercontinuous hypersmooth Schwarzschild line element transformation.
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 non-Standard Characterization of the norm of free Ultrafilters
A nonstandard set theory
A nonstandard treatment with quantities
A note on the Mac Dowell-Specker theorem
A note on Δ₁ induction and Σ₁ collection
Slaman recently proved that Σₙ collection is provable from Δₙ induction plus exponentiation, partially answering a question of Paris. We give a new version of this proof for the case n = 1, which only requires the following very weak form of exponentiation: " exists for some y sufficiently large that x is smaller than some primitive recursive function of y".
A sequence of theories for arithmetic whose union is complete
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.)