Page 1 Next

Displaying 1 – 20 of 198

Showing per page

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.

A Radon-Nikodym derivative for positive linear functionals

E. de Amo, M. Díaz Carrillo (2009)

Studia Mathematica

An exact Radon-Nikodym derivative is obtained for a pair (I,J) of positive linear functionals, with J absolutely continuous with respect to I, using a notion of exhaustion of I on elements of a function algebra lattice.

A simple proof of the Borel extension theorem and weak compactness of operators

Ivan Dobrakov, Thiruvaiyaru V. Panchapagesan (2002)

Czechoslovak Mathematical Journal

Let T be a locally compact Hausdorff space and let C 0 ( T ) be the Banach space of all complex valued continuous functions vanishing at infinity in T , provided with the supremum norm. Let X be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of X -valued σ -additive Baire measures on T is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear map u C 0 ( T ) X when...

Algebraic genericity of strict-order integrability

Luis Bernal-González (2010)

Studia Mathematica

We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space L p ( μ , X ) (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of L p ( μ , X ) (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological space and...

Approximating Radon measures on first-countable compact spaces

Grzegorz Plebanek (2000)

Colloquium Mathematicae

The assertion every Radon measure defined on a first-countable compact space is uniformly regular is shown to be relatively consistent. We prove an analogous result on the existence of uniformly distributed sequences in compact spaces of small character. We also present two related examples constructed under CH.

Borel extensions of Baire measures

J. Aldaz (1997)

Fundamenta Mathematicae

We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space is Mařík,...

Currently displaying 1 – 20 of 198

Page 1 Next