Papers by Giuseppina Barbieri
Rendiconti del Circolo Matematico di Palermo, 2013
We prove a Lyapunov type theorem for closed pseudo-non-injective modular measures on pseudo-D-lat... more We prove a Lyapunov type theorem for closed pseudo-non-injective modular measures on pseudo-D-lattices and we prove that any closed modular measure can be decomposed into the sum of a Lyapunov modular measure and an anti-Lyapunov modular measure.
ABSTRACT We prove a Hahn decomposition theorem for σ-additive modular measures on σ-complete latt... more ABSTRACT We prove a Hahn decomposition theorem for σ-additive modular measures on σ-complete lattice ordered effect algebras. As a consequence, we establish an isomorphism between the space of all bounded real-valued modular measures on a such structure and the space of all completely additive measures on a suitable Boolean algebra. Another consequence is a Uhl type theorem concerning relative compactness and convexity of the range of nonatomic modular measures with values in Banach spaces.
Mathematische Nachrichten, 2008
For a recursively defined sequence u := (un) of integers, we describe the subgroup tu(T) of the e... more For a recursively defined sequence u := (un) of integers, we describe the subgroup tu(T) of the elements x of the circle group T satisfying limn unx = 0. More attention is dedicated to the sequences satisfying a secondorder recurrence relation. In this case, we show that the size and the free-rank of tu(T) is determined by the asymptotic behaviour of the ratios qn = un u n−1 and we extend previous results of G. Larcher, C. Kraaikamp, and P. Liardet obtained from continued fraction expansion.
Functional Analysis and Economic Theory, 1998
Soft Computing - A Fusion of Foundations, Methodologies and Applications, 2003
ABSTRACT As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes... more ABSTRACT As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes of fuzzy sets with T-measures. They made the first steps towards a characterization of monotonic real-valued T-measures for a Frank triangular norm T. Later on, Mesiar and the authors of this paper found independently two generalizations, one for vector-valued T-measures with respect to Frank t-norms (in particular for nonmonotonic ones) [3], the other for monotonic real-valued T-measures with respect to general strict t-norms [15]. Here we present a common generalization – a characterization of nonmonotonic T-measures with respect to an arbitrary strict t-norm. Moreover, we prove this for vector-valued T-measures. Using this characterization, we generalize Ljapunov Theorem to this context.
Algebra Universalis, 2009
We prove an algebraic and a topological decomposition theorem for complete D-lattices (i.e., latt... more We prove an algebraic and a topological decomposition theorem for complete D-lattices (i.e., lattice-ordered effect algebras). As a consequence, we obtain a Hammer-Sobczyk type decomposition theorem for modular measures on D-lattices.
Mathematica Slovaca, 1999
Functional Analysis and Economic Theory, 1998
We give an alternative proof of a Cafiero type theorem for mea-sures on effect algebras.
We characterize T-measures on weakly generated tribes, where T is a strict tri- angular norm and ... more We characterize T-measures on weakly generated tribes, where T is a strict tri- angular norm and we give a Liapunoff Theorem for these measures. This gen- eralizes previous results obtained for monotonic T-measures or for Frank tri- angular norms.
Journal of Electrical Engineering
We obtain for modular measures on lattice ordered effect algebras the classical theorem of Dieudo... more We obtain for modular measures on lattice ordered effect algebras the classical theorem of Dieudonné related to convergent sequences of regular maps. 1 Introduction In 1933 Nikodm [10] proved the well-known Vitali-Hahn-Saks theorem, namely "If a sequence of Borel measures converges pointwise to a map µ, then µ is a Borel measure." In 1951 Dieudonné proved the following more general theorem: "If a sequence of regular measures defined on Borel sets of a compact metrizable space converges on every open set, then it converges on every Borel sets. In this case, the sequence is uniformly regular". This theorem generalizes Nikodm' s theorem if one substitutes the pointwise convergence on the Borel σ-algebra for the analogous condition on open sets provided a regularity assumption and a topological condition on the space are satisfied. Brooks in [6] generalizes this theorem to the case the space is either compact or the space is normal and the sequence is uniformly b...
Applied General Topology
We study the sequences of integers (u n ) that converge to 0 in some precompact group topology on... more We study the sequences of integers (u n ) that converge to 0 in some precompact group topology on Z and the properties of the finest topology with this property when (u n ) satisfies a linear recurrence relation with bounded coe cients. Some of the results are extended to the case of sequences in arbitrary Abelian groups.
For a subgroup H of a topological abelian group G denote by group S(H) the set of all sequences o... more For a subgroup H of a topological abelian group G denote by group S(H) the set of all sequences of integers (u n ) such that u n h → 0 for every h ∈ H; H is called t-dense if S(H) = S(G). Motivated by a question of Raczkowski we explore the existence of small (with respect to size or measure) t-dense subgroups of topological abelian groups.
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Papers by Giuseppina Barbieri