We present pseudo Vitali spaces as lattices with a partially defined operation,+ , that is not necessarily commutative. We show that they can be embedded into l-groups, and we give a categorical equivalence of the category of pseudo Vitali spaces. Studying states on Vitali spaces with strong unit, we show that every Dedekind sigma-complete Vitali space is an epimorphic image of a Vitali space of bounded functions where the operations on functions are defined pointwise.
Representations of pseudo Vitali spaces and Loomis-Sikorski Theorem
VENTRIGLIA, FLAVIA
2011
Abstract
We present pseudo Vitali spaces as lattices with a partially defined operation,+ , that is not necessarily commutative. We show that they can be embedded into l-groups, and we give a categorical equivalence of the category of pseudo Vitali spaces. Studying states on Vitali spaces with strong unit, we show that every Dedekind sigma-complete Vitali space is an epimorphic image of a Vitali space of bounded functions where the operations on functions are defined pointwise.File in questo prodotto:
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