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Articles

Representations of pseudo Vitali spaces and Loomis–Sikorski theorem

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Pages 39-59 | Received 15 Oct 2008, Accepted 25 Apr 2009, Published online: 21 Jul 2010
 

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 σ-complete Vitali space is an epimorphic image of a Vitali space of bounded functions where the operations on functions are defined pointwise.

Acknowledgements

This paper has been supported by the Centre of Excellence SAS, the grant VEGA No 2/0032/09 SAV, the Slovak Research and Development Agency under contract No. APVV-0071-06, MURST, project ‘Analisi Reale’.

Notes

Additional information

Notes on contributors

F. Ventriglia

1 1. [email protected]

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