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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)


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 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.

A note on Δ₁ induction and Σ₁ collection

Neil Thapen (2005)

Fundamenta Mathematicae

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: " x y exists for some y sufficiently large that x is smaller than some primitive recursive function of y".

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