ABSTRACT Let L be a pseudo-D-lattice. We prove that the exhaustive lattice uniformities on L whic... more ABSTRACT Let L be a pseudo-D-lattice. We prove that the exhaustive lattice uniformities on L which makes the operations of L uniformly continuous form a Boolean algebra isomorphic to the centre of a suitable complete pseudo-D-lattice associated to L. As a consequence, we obtain decomposition theorems—such as Lebesgue and Hewitt—Yosida decompositions—and control theorems—such as Bartle—Dunford—Schwartz and Rybakov theorems—for modular measures on L.
We introduce the notion of ∧-projection in order to extend to d0-algebras the concept of Kalmbach... more We introduce the notion of ∧-projection in order to extend to d0-algebras the concept of Kalmbach measurable elements with respect to an outer measure μ. We prove, in case μ is faithful, that Kalmbach measurable ∧-projections are quasi-central, thus generalizing a result known for orthomodular lattices, and recently extended to D-lattices.
We prove linearity theorems for modular measures on pseudo-D-lattices (= lattice ordered pseudo-e... more We prove linearity theorems for modular measures on pseudo-D-lattices (= lattice ordered pseudo-effect algebras) and we study the consequences for the core of measure games.
ABSTRACT Nonatomic finitely additive correspondences with values in B-convex Banach spaces necess... more ABSTRACT Nonatomic finitely additive correspondences with values in B-convex Banach spaces necessarily have the property that the closure of the range is convex. For this one assumes that the correspondences are of bounded variation.
We define the center C(A) of a d0-algebra A as a set of self-mappings on A. The center can be reg... more We define the center C(A) of a d0-algebra A as a set of self-mappings on A. The center can be regarded as the set of all possible d0-subdirect factors of A which are subalgebras of A. we show that C(A) is always a Boolean algebra. we also show that C(A) admits an embedding in the power Aκ, where κ is the cofinality of A. In case κ = 1 (i.e. A is a D-lattice) we reobtain the well-known fact that C(A) is a subalgebra of A.
We prove a general decomposition theorem for $$d_0$$d0-algebras, from which we derive a Hahn deco... more We prove a general decomposition theorem for $$d_0$$d0-algebras, from which we derive a Hahn decomposition-type theorem for $$d_0$$d0-measures on these structures. This generalizes the similar result known for modular measures on D-lattices and also gives, as a particular case, a Hahn decomposition-type theorem for measures on cancellative BCK-algebras.
ABSTRACT The range of a finitely additive closed-valued nonatomic correspondence is convex if the... more ABSTRACT The range of a finitely additive closed-valued nonatomic correspondence is convex if the domain is a σ-algebra.
Rendiconti Del Circolo Matematico Di Palermo, Aug 5, 2019
We prove that a closed $$\hbox {d}_{\text {0}}$$ -measure on a $$\hbox {d}_{\text {0}}$$ -algebra... more We prove that a closed $$\hbox {d}_{\text {0}}$$ -measure on a $$\hbox {d}_{\text {0}}$$ -algebra can be decomposed into the sum of a Lyapunov $$\hbox {d}_{\text {0}}$$ -measure and an anti-Lyapunov $$\hbox {d}_{\text {0}}$$ -measure.
ABSTRACT Let L be a pseudo-D-lattice. We prove that the exhaustive lattice uniformities on L whic... more ABSTRACT Let L be a pseudo-D-lattice. We prove that the exhaustive lattice uniformities on L which makes the operations of L uniformly continuous form a Boolean algebra isomorphic to the centre of a suitable complete pseudo-D-lattice associated to L. As a consequence, we obtain decomposition theorems—such as Lebesgue and Hewitt—Yosida decompositions—and control theorems—such as Bartle—Dunford—Schwartz and Rybakov theorems—for modular measures on L.
We introduce the notion of ∧-projection in order to extend to d0-algebras the concept of Kalmbach... more We introduce the notion of ∧-projection in order to extend to d0-algebras the concept of Kalmbach measurable elements with respect to an outer measure μ. We prove, in case μ is faithful, that Kalmbach measurable ∧-projections are quasi-central, thus generalizing a result known for orthomodular lattices, and recently extended to D-lattices.
We prove linearity theorems for modular measures on pseudo-D-lattices (= lattice ordered pseudo-e... more We prove linearity theorems for modular measures on pseudo-D-lattices (= lattice ordered pseudo-effect algebras) and we study the consequences for the core of measure games.
ABSTRACT Nonatomic finitely additive correspondences with values in B-convex Banach spaces necess... more ABSTRACT Nonatomic finitely additive correspondences with values in B-convex Banach spaces necessarily have the property that the closure of the range is convex. For this one assumes that the correspondences are of bounded variation.
We define the center C(A) of a d0-algebra A as a set of self-mappings on A. The center can be reg... more We define the center C(A) of a d0-algebra A as a set of self-mappings on A. The center can be regarded as the set of all possible d0-subdirect factors of A which are subalgebras of A. we show that C(A) is always a Boolean algebra. we also show that C(A) admits an embedding in the power Aκ, where κ is the cofinality of A. In case κ = 1 (i.e. A is a D-lattice) we reobtain the well-known fact that C(A) is a subalgebra of A.
We prove a general decomposition theorem for $$d_0$$d0-algebras, from which we derive a Hahn deco... more We prove a general decomposition theorem for $$d_0$$d0-algebras, from which we derive a Hahn decomposition-type theorem for $$d_0$$d0-measures on these structures. This generalizes the similar result known for modular measures on D-lattices and also gives, as a particular case, a Hahn decomposition-type theorem for measures on cancellative BCK-algebras.
ABSTRACT The range of a finitely additive closed-valued nonatomic correspondence is convex if the... more ABSTRACT The range of a finitely additive closed-valued nonatomic correspondence is convex if the domain is a σ-algebra.
Rendiconti Del Circolo Matematico Di Palermo, Aug 5, 2019
We prove that a closed $$\hbox {d}_{\text {0}}$$ -measure on a $$\hbox {d}_{\text {0}}$$ -algebra... more We prove that a closed $$\hbox {d}_{\text {0}}$$ -measure on a $$\hbox {d}_{\text {0}}$$ -algebra can be decomposed into the sum of a Lyapunov $$\hbox {d}_{\text {0}}$$ -measure and an anti-Lyapunov $$\hbox {d}_{\text {0}}$$ -measure.
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Papers by Anna Avallone