Pseudo-D-lattices and separating points of measures

Avallone, Anna; Vitolo, Paolo

doi:10.1016/j.fss.2015.06.015

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Cited by 3 publications

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“…Guiseppina Barbieri [3] proved an extension theorem for modular measures on lattice ordered algebras and used this theorem to obtain analogues of the Nikodym theorem and other theorems. Avallone and Vitolo [1] obtained results about a modular measure on a pseudo-D-lattice, and Avallone, De Simone and Vitolo [2] proved a Caratheodory type extension theorem for σ-additive exhaustive modular measures on σ-continuous pseudo-D-lattices.…”

Section: Introductionmentioning

confidence: 98%

Measure on a Lattice of Infinite Tuples of Real Numbers

Sookoo

2024

Pan-Amer. J. Math.

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We consider the analogue of measure on a ring of sets, by defining a lattice-measure on a lattice-ring of elements of a lattice of infinite tuples of real numbers. We obtain various results about the convergence of sequences of tuples in the lattice with respect to the lattice-measure and use these results to show that the limit of a convergent sequence in a lattice sigma-ring is also in the lattice sigma-ring under certain conditions.

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Section: Introductionmentioning

confidence: 98%