55 research outputs found
Subdifferential calculus for invariant linear ordered vector space-valued operators and applications
We give a direct proof of sandwich-type theorems for linear invariant partially ordered vector space operators in the setting of convexity. As consequences, we deduce equivalence results between sandwich, Hahn-Banach, separation and Krein-type extension theorems, Fenchel duality, Farkas and Kuhn-Tucker-type minimization results and subdifferential formulas in the context of invariance. As applications, we give Tarski-type extension theorems and related examples for vector lattice-valued invariant probabilities, defined on suitable kinds of events
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
The symmetric Choquet integral with respect to Riesz-space-valued capacities
summary:A definition of “Šipoš integral” is given, similarly to [3],[5],[10], for real-valued functions and with respect to Dedekind complete Riesz-space-valued “capacities”. A comparison of Choquet and Šipoš-type integrals is given, and some fundamental properties and some convergence theorems for the Šipoš integral are proved
Dieudonné-type theorems for lattice group-valued -triangular set functions
summary:Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for -triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems
Kuelbs-Steadman spaces for Banach space-valued measures
We introduce Kuelbs-Steadman-type spaces for real-valued functions, with
respect to countably additive measures, taking values in Banach spaces. We
investigate their main properties and embeddings in -type spaces,
considering both the norm associated to norm convergence of the involved
integrals and that related to weak convergence of the integrals.Comment: 12 page
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