Search results for " weak convergence"

showing 2 items of 2 documents

Convergence for varying measures in the topological case

2023

In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.

Mathematics - Functional Analysis28B05Primary 28B20 Secondary 26E25 26A39 28B05 46G10 54C60 54C6526A39setwise convergence vaguely convergence weak convergence of measures locally compact Hausdorff space Vitali's TheoremSettore MAT/05 - Analisi Matematica54C60FOS: MathematicsPrimary 28B20Secondary 26E2554C65Functional Analysis (math.FA)46G10
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VARIANTS OF A SELECTION PRINCIPLE FOR SEQUENCES OF REGULATED AND NON-REGULATED FUNCTIONS

2008

Let $T$ be a nonempty subset of $\RB$, $X$ a metric space with metric $d$ and $X^T$ the set of all functions mapping $T$ into $X$. Given $\vep>0$ and $f\in X^T$, we denote by $N(\vep,f,T)$ the least upper bound of those $n\in\NB$, for which there exist numbers $s_1,\dots,s_n,t_1,\dots,t_n$ from $T$ such that $s_1\vep$ for all $i=1,\dots,n$ ($N(\vep,f,T)=0$ if there are no such $n$'s). The following pointwise selection principle is proved: {\em If a sequence of functions\/ $\{f_j\}_{j=1}^\infty\subset X^T$ is such that the closure in $X$ of the sequence\/ $\{f_j(t)\}_{j=1}^\infty$ is compact for each $t\in T$ and\/ $\limsup_{j\to\infty}N(\vep,f_j,T)0$, then\/ $\{f_j\}_{j=1}^\infty$ contains …

Pointwise convergence selection principle regulated function generalized variation metric space metric semigroup Banach space double sequence weak convergence almost everywhere convergence.Settore MAT/05 - Analisi MatematicaSelection principleComputational biologyMathematics
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