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Some fine properties of sets with finite perimeter in Wiener spaces

Michele Miranda Jr. (2014)

Banach Center Publications

In this paper we give a brief overview on the state of art of developments of Geometric Measure Theory in infinite-dimensional Banach spaces. The framework is given by an abstract Wiener space, that is a separable Banach space endowed with a centered Gaussian measure. The focus of the paper is on the theory of sets with finite perimeter and on their properties; this choice was motivated by the fact that most of the good properties of functions of bounded variation can be obtained, thanks to coarea...

Some problems for measures on non-standard algebraic structures

Maria Gabriella Graziano (2000)

Bollettino dell'Unione Matematica Italiana

Nell'ultimo ventennio tutta una serie di lavori è stata rivolta allo studio delle misure su strutture algebriche più generali delle algebre di Boole, come i poset e i reticoli ortomodulari, le effect algebras, le BCK-algebras. La teoria così ottenuta interessa l'analisi funzionale, il calcolo delle probabilità e la topologia, più recentemente la teoria delle decisioni. Si presentano alcuni risultati relativi a misure su strutture algebriche non-standard analizzando, in particolare, gli aspetti topologici...

Some remarks on Gleason measures

P. De Nápoli, M. C. Mariani (2007)

Studia Mathematica

This work is devoted to generalizing the Lebesgue decomposition and the Radon-Nikodym theorem to Gleason measures. For that purpose we introduce a notion of integral for operators with respect to a Gleason measure. Finally, we give an example showing that the Gleason theorem does not hold in non-separable Hilbert spaces.

Sommes vectorielles d'ensembles de mesure nulle

Michel Talagrand (1976)

Annales de l'institut Fourier

Soit G un groupe localement compact abélien ou un groupe de Lie et A un compact parfait de G . Il existe alors un compact B de mesure de Haar nulle tel que A B = { a b ; a ∈ A , b ∈ B } soit d’intérieur non vide. En particulier si G est métrisable, les seuls ensembles analytiques tels que A B soit de mesure nulle dès que B l’est, sont dénombrables.

Stochastic integration of functions with values in a Banach space

J. M. A. M. van Neerven, L. Weis (2005)

Studia Mathematica

Let H be a separable real Hilbert space and let E be a real Banach space. In this paper we construct a stochastic integral for certain operator-valued functions Φ: (0,T) → ℒ(H,E) with respect to a cylindrical Wiener process W H ( t ) t ∈ [ 0 , T ] . The construction of the integral is given by a series expansion in terms of the stochastic integrals for certain E-valued functions. As a substitute for the Itô isometry we show that the square expectation of the integral equals the radonifying norm of an operator which is...

Strict topologies as topological algebras

Surjit Singh Khurana (2001)

Czechoslovak Mathematical Journal

Let X be a completely regular Hausdorff space, C b ( X ) the space of all scalar-valued bounded continuous functions on X with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally m -convex.

Strong Fubini axioms from measure extension axioms

Piotr Zakrzewski (1992)

Commentationes Mathematicae Universitatis Carolinae

It is shown that measure extension axioms imply various forms of the Fubini theorem for nonmeasurable sets and functions in Radon measure spaces.

Structure of measures on topological spaces.

José L. de María, Baltasar Rodríguez Salinas (1989)

Revista Matemática de la Universidad Complutense de Madrid

The Radon spaces of type (T), i.e., topological spaces for which every finite Borel measure on Omega is T-additive and T-regular are characterized. The class of these spaces is very wide and in particular it contains the Radon spaces. We extend the results of Marczewski an Sikorski to the sygma-metrizable spaces and to the subsets of the Banach spaces endowed with the weak topology. Finally, the completely additive families of measurable subsets related with the works of Hansell, Koumoullis, and...

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