(adsbygoogle = window.adsbygoogle || []).push({}); Does this define "measure"?

I've been reading the following paper:

Scaled Boolean Algebra, by Michael Hardy, arXiv:math/0203249v1.

and I'm wondering how much his efforts prove. He seems to prove that Boolean Algebras (such as exist in set theory and Propositional logic) can be mapped to math if the variables used (sets in set theory and propositions in logic) are part of a partially ordered set. If this partial ordering prescribes that some variables are larger or have more weight than others, then this weight can be mapped to relative increasing numerical values. He then goes on to show that this also allows set theoretic union or logical disjunction to be mapped to addition and set theoretic intersection or logical conjunction to be mapped to multiplication. And all this seems to be a way of defining a measure on sets in what seems to be the usual way. Is this the only way to map set theory and/or Propositional logic to numerical math operations? Are his efforts necessary to define a measure? Thanks.

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# Does this define measure ?

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