Some observations and results concerning submeasures on Boolean algebras

Selim, Omar (2012) Some observations and results concerning submeasures on Boolean algebras. Doctoral thesis, University of East Anglia .

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Abstract

We investigate submeasures on Boolean algebras in the context of Maharam's problem and
its solution. We generalise results that were originally proved for measures, to cases where
additivity is not present. We investigate Talagrand's construction of a pathological exhaustive
submeasure, attempting to give a more explicit description of this submeasure and we also
consider some of its forcing properties. We consider the forcing consisting of submeasures
that have as their domain a �nite subalgebra of the countable atomless Boolean algebra.
We �nd and investigate a linear association between the real vector space of all real-valued
functionals on the countable atomless Boolean algebra, which includes the collection of all
submeasures, and the space of all signed �nitely additive measures on this Boolean algebra.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Zoe White
Date Deposited: 07 Feb 2014 10:31
Last Modified: 07 Feb 2014 10:31
URI: https://ueaeprints.uea.ac.uk/id/eprint/41414
DOI:

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