210 research outputs found
A note on set-valued Henstock--McShane integral in Banach (lattice) space setting
We study Henstock-type integrals for functions defined in a Radon measure
space and taking values in a Banach lattice . Both the single-valued case
and the multivalued one are considered (in the last case mainly -valued
mappings are discussed). The main tool to handle the multivalued case is a
R{\aa}dstr\"{o}m-type embedding theorem established in [50]: in this way we
reduce the norm-integral to that of a single-valued function taking values in
an -space and we easily obtain new proofs for some decomposition results
recently stated in [33,36], based on the existence of integrable selections.
Also the order-type integral has been studied: for the single-valued case
some basic results from [21] have been recalled, enlightning the differences
with the norm-type integral, specially in the case of -space-valued
functions; as to multivalued mappings, a previous definition ([6]) is restated
in an equivalent way, some selection theorems are obtained, a comparison with
the Aumann integral is given, and decompositions of the previous type are
deduced also in this setting. Finally, some existence results are also
obtained, for functions defined in the real interval .Comment: This work has been modified both as regards the drawing that with
regard to the assumptions. A new version is contained in the paper
arXiv:1503.0828
Existence of weak solutions to stochastic evolution inclusions
We consider the Cauchy problem for a semilinear stochastic differential
inclusion in a Hilbert space. The linear operator generates a strongly
continuous semigroup and the nonlinear term is multivalued and satisfies a
condition which is more heneral than the Lipschitz condition. We prove the
existence of a mild solution to this problem. This solution is not "strong" in
the probabilistic sense, that is, it is not defined on the underlying
probability space, but on a larger one, which provides a "very good extension"
in the sense of Jacod and Memin. Actually, we construct this solution as a
Young measure, limit of approximated solutions provided by the Euler scheme.
The compactness in the space of Young measures of this sequence of approximated
solutions is obtained by proving that some measure of noncompactness equals
zero
Impulsive feedback control : a constructive approach
Tese de doutoramento. Engenharia Electrotécnica e de Computadores. Faculdade de Engenharia. Universidade do Porto. 200
Quantitative Coding and Complexity Theory of Compact Metric Spaces
Specifying a computational problem requires fixing encodings for input and
output: encoding graphs as adjacency matrices, characters as integers, integers
as bit strings, and vice versa. For such discrete data, the actual encoding is
usually straightforward and/or complexity-theoretically inessential (up to
polynomial time, say); but concerning continuous data, already real numbers
naturally suggest various encodings with very different computational
properties. With respect to qualitative computability, Kreitz and Weihrauch
(1985) had identified ADMISSIBILITY as crucial property for 'reasonable'
encodings over the Cantor space of infinite binary sequences, so-called
representations [doi:10.1007/11780342_48]: For (precisely) these does the
sometimes so-called MAIN THEOREM apply, characterizing continuity of functions
in terms of continuous realizers.
We rephrase qualitative admissibility as continuity of both the
representation and its multivalued inverse, adopting from
[doi:10.4115/jla.2013.5.7] a notion of sequential continuity for
multifunctions. This suggests its quantitative refinement as criterion for
representations suitable for complexity investigations. Higher-type complexity
is captured by replacing Cantor's as ground space with Baire or any other
(compact) ULTRAmetric space: a quantitative counterpart to equilogical spaces
in computability [doi:10.1016/j.tcs.2003.11.012]
Monotone approximation of measurable multifunctions by simple multifunctions
summary:We investigate the problem of approximation of measurable multifunctions by monotone sequences of measurable simple ones. Our main tool is the Marczewski function, i.e., the characteristic function of a sequence of sets
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