1,720,988 research outputs found
Strong uniform continuity and filter exhaustiveness of nets of cone metric space-valued functions
No full textWe give necessary and sufficient conditions for (strong uniform) continuity of the limit of a pointwise convergent net of cone
metric space-valued functions. In this framework we consider several types of convergence (Alexandroff, Arzelà, sticky, strong uniform)
in the filter context and some kinds of filter exhaustiveness
On filter alpha-convergence and exhaustiveness of function nets in lattice groups and applications
No full textWe consider (strong uniform) continuity of the limit of a pointwise convergent net of lattice group-valued functions, (strong weak) exhaustiveness and (strong) alpha convergence with respect to a pair of filters, which in the setting of nets are more natural than the corresponding notions formulated with respect to a single filter. Some comparison results are given between such concepts, in
connection with suitable properties of filters. Moreover, some modes of filter (strong uniform) continuity for lattice group-valued
functions are investigated, giving some characterization. As an application, we get some Ascoli-type theorem in an abstract setting,
extending earlier results to the context of filter alpha-convergence
Asymmetric ascoli-type theorems and filter exhaustiveness
No full textWe prove some Ascoli-type theorem, giving a necessary and sufficient condition for forward compactness of sets of functions, defined and with values in asymmetric metric spaces
Some new results on ideal limit theorems in l-groups
No full textWe present some limit theorems for sequences of
measures, taking values in l-groups, in the setting
of ideal convergence. We use the tool of ideal exhaustiveness
in order to prove some results on uniform s-boundedness, uniform sigma-additivity, uniform absolute continuity and uniform regularity of a suitable subsequence of the given one, whose indexes belong to the dual filter associated to the ideal involved. We observe that, in general, ideal exhaustiveness is a condition, which cannot be dropped and we give an example about it. We deal with Frechet-Nikodym topologies and submeasures
Ideal exhaustiveness and limit theorems for l-group-valued measures
No full textIn this paper we present some results about existence and sigma-additivity of suitable limit measures, taking values in l-groups, in the setting of ideal convergence. We use the tool of ideal exhaustiveness, extending some earlier results, which were given in the real setting
Brooks-Jewett-type theorems for the pointwise ideal convergence of measures with values in l-groups
No full textSome Brooks-Jewett, Vitali-Hahn-Saks and Nikodym convergence-type theorems in the context of l-groups with respect to ideal convergence are proved. Moreover, an example is given, in which it is shown that in general results analogous to these kinds of limit theorems do not hold, when pointwise convergence of the measure involved is replaced by the corresponding ideal pointwise convergence
Limit theorems in l-groups with respect to D-convergence
No full textSome Schur, Vitali-Hahn-Saks and Nikodym convergence theorems for l-group-valued measures are given in the context of (D)-convergence. We consider both the sigma-additive and the finitely additive case. The pointwise convergence of the measures involved is assumed to be with respect to a common regulator, while the concepts of sigma-additivity and strong boundedness are formulated similarly as the corresponding classical ones (and not with respect to a same regulator)
Ideal convergence and divergence of nets in l-groups
No full textIn this paper we introduce the I- and I^*-convergence and divergence of nets in l-groups. We prove some theorems relating
different types of convergence/divergence for nets in l-group setting, in relation with ideals. We consider both order and (D)-convergence.
By using basic properties of order sequences,
some fundamental properties, Cauchy-type characterizations
and comparison results are derived.
We prove that I^-convergence/divergence implies
I-convergence/divergence for every ideal, admissible for
the set of indexes with respect to which the net involved is directed, and we investigate a class of ideals for which the converse implication holds
Ideal exhaustiveness, continuity and alpha-convergence for latticegroup-valued functions
No full textWe examine some fundamental properties of ideal exhaustiveness, in the context of l-groups with respect to (D)-convergence. We give some necessary and/or sufficient conditions, in order that the limit measure is continuous (with respect to a common regulator), and we investigated some particular properties of the ideals of the set of all natural numbers
Ideal exhaustiveness, weak convergence and weak compactness in Banach spaces
No full textSome types of compactness in the ideal context are defined and relations between ideal exhaustiveness and equicontinuity of measures are investigated. As applications, some versions of limit theorems involving ideal pointwise convergence of measure sequence and some weak compactness results related to integral functionals are presented
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