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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 noncommutative version of a Theorem of Marczewski for submeasures

Paolo de Lucia, Pedro Morales (1992)

Studia Mathematica

It is shown that every monocompact submeasure on an orthomodular poset is order continuous. From this generalization of the classical Marczewski Theorem, several results of commutative Measure Theory are derived and unified.

Borel extensions of Baire measures in ZFC

Menachem Kojman, Henryk Michalewski (2011)

Fundamenta Mathematicae

We prove: 1) Every Baire measure on the Kojman-Shelah Dowker space admits a Borel extension. 2) If the continuum is not real-valued-measurable then every Baire measure on M. E. Rudin's Dowker space admits a Borel extension. Consequently, Balogh's space remains the only candidate to be a ZFC counterexample to the measure extension problem of the three presently known ZFC Dowker spaces.

Convergence and submeasures in Boolean algebras

Tomáš Jech (2018)

Commentationes Mathematicae Universitatis Carolinae

A Boolean algebra carries a strictly positive exhaustive submeasure if and only if it has a sequential topology that is uniformly Fréchet.

Dividing measures and narrow operators

Volodymyr Mykhaylyuk, Marat Pliev, Mikhail Popov, Oleksandr Sobchuk (2015)

Studia Mathematica

We use a new technique of measures on Boolean algebras to investigate narrow operators on vector lattices. First we prove that, under mild assumptions, every finite rank operator is strictly narrow (before it was known that such operators are narrow). Then we show that every order continuous operator from an atomless vector lattice to a purely atomic one is order narrow. This explains in what sense the vector lattice structure of an atomless vector lattice given by an unconditional basis is far...

Examples of ε-exhaustive pathological submeasures

Ilijas Farah (2004)

Fundamenta Mathematicae

For any given ε > 0 we construct an ε-exhaustive normalized pathological submeasure. To this end we use potentially exhaustive submeasures and barriers of finite subsets of ℕ.

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