405 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
Modular convergence theorems for integral operators in the context of filter exhaustiveness and applications
No full textWe prove some modular convergence theorems for nonlinear Urysohn-type integral operators, applying filter convergence of sequences of functions. We use the tool of filter exhaustiveness, and we give several applications, in particular to Mellin operators, including moment, Mellin-Poisson-Cauchy and Mellin-Gauss-Weierstrass operators. We give some example, in which we show that our results are proper extensions of the classical ones
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
Asymmetric ascoli-type theorems and filter exhaustiveness
No full textWe prove an Ascoli-type theorem, giving a necessary and sufficient condition for forward compactness of sets of functions, defined and with values in asymmetric metric spaces. Furthermore, we pose some open problems. © 2015 A. Boccuto and X. Dimitriou
Ideal limit theorems and their equivalence in l-group setting
No full textWe prove some equivalence results between
limit theorems for sequences of
l-group-valued measures, with respect to
order ideal convergence. A fundamental role is
played by the tool of uniform ideal
exhaustiveness of a measure sequence already
introduced for the real case or more generally
for the Banach space case in our recent papers,
to get some results on uniform
strong boundedness and uniform countable
additivity. We consider both the case in which
strong boundedness, countable additivity and the
related concepts are formulated with respect
to a common order sequence and the context in
which these notions are given in a classical like
setting, that is not necessarily with respect to a
same (O)-sequence. We show that, in general,
uniform ideal exhaustiveness cannot be omitted.
Finally we pose some open problems
Modes of ideal continuity of l-group-valued measures
No full textIn this paper we deal with
(ideal) continuity of lattice
group-valued finitely additive measures, and prove
some basic properties and comparison results. We
investigate the relations between
different modes of ideal continuity, and give
some characterization.
Finally we pose some open problems
Modular filter convergence theorems for Urysohn integral operators and applications
No full textWe prove some versions of modular convergence theorems for nonlinear Urysohn-type integral operators with respect to filter convergence.
We consider pointwise filter convergence of functions giving also some applications to linear and nonlinear Mellin operators.
We show that our results are strict extensions of the corresponding classical ones and we give some examples
concerning Mellin-Gauss-Weierstrass-type operators
Convergence Theorems for Lattice Group-Valued Measures
No full text"Convergence Theorems for Lattice Group-valued Measures" explains limit and boundedness theorems for measures taking values in abstract structures. The book begins with a historical survey about these topics since the beginning of the last century, moving on to basic notions and preliminaries on filters/ideals, lattice groups, measures and tools which are featured in the rest of this text. Readers will also find a survey on recent classical results about limit, boundedness and extension theorems for lattice group-valued measures followed by information about recent developments on these kinds of theorems and several results in the setting of filter/ideal convergence. In addition, each chapter has a general description of the topics and an appendix on random variables, concepts and lattices is also provided. Thus readers will benefit from this book through an easy-to-read historical survey about all the problems on convergence and boundedness theorems, and the techniques and tools which are used to prove the main results. The book serves as a primer for undergraduate, postgraduate and Ph. D. students on mathematical lattice and topological groups and filters, and a treatise for expert researchers whose aim to extend their knowledge base
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
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