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Continuous linear functionals on the space of Borel vector measures

Pola Siwek (2008)

Annales Polonici Mathematici

We study properties of the space ℳ of Borel vector measures on a compact metric space X, taking values in a Banach space E. The space ℳ is equipped with the Fortet-Mourier norm | | · | | and the semivariation norm ||·||(X). The integral introduced by K. Baron and A. Lasota plays the most important role in the paper. Investigating its properties one can prove that in most cases the space ( , | | · | | ) * is contained in but not equal to the space (ℳ,||·||(X))*. We obtain a representation of the continuous functionals on...

Continuous selection theorems

Michał Kisielewicz (2005)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.

Contracting-on-Average Baker Maps

Michał Rams (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.

Controlled convergence theorems for Henstock-Kurzweil-Pettis integral on m -dimensional compact intervals

Sokol B. Kaliaj, Agron D. Tato, Fatmir D. Gumeni (2012)

Czechoslovak Mathematical Journal

In this paper we use a generalized version of absolute continuity defined by J. Kurzweil, J. Jarník, Equiintegrability and controlled convergence of Perron-type integrable functions, Real Anal. Exch. 17 (1992), 110–139. By applying uniformly this generalized version of absolute continuity to the primitives of the Henstock-Kurzweil-Pettis integrable functions, we obtain controlled convergence theorems for the Henstock-Kurzweil-Pettis integral. First, we present a controlled convergence theorem for...

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.

Convergence and uniqueness problems for Dirichlet forms on fractals

Roberto Peirone (2000)

Bollettino dell'Unione Matematica Italiana

M 1 è un particolare operatore di minimizzazione per forme di Dirichlet definite su un sottoinsieme finito di un frattale K che è, in un certo senso, una sorta di frontiera di K . Viene talvolta chiamato mappa di rinormalizzazione ed è stato usato per definire su K un analogo del funzionale u grad u 2 e un moto Browniano. In questo lavoro si provano alcuni risultati sull'unicità dell'autoforma (rispetto a M 1 ), e sulla convergenza dell'iterata di M 1 rinormalizzata. Questi risultati sono collegati con l'unicità...

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