Preprint: Algebraic theory of vector-valued integration

Preprint: Algebraic theory of vector-valued integration

[Rory Lucyshyn-Wright]

A preprint of my paper "Algebraic theory of vector-valued integration" is 
now available at

http://arxiv.org/abs/1108.2913

This paper subsumes the content of my talk of the same name at CT2011. 
An abstract is included below.

Your comments are welcome.

Regards,
Rory Lucyshyn-Wright

Abstract:  We define a monad M on a category of measurable bornological 
sets, and we show how this monad gives rise to a theory of vector-valued 
integration that is related to the notion of Pettis integral.  We show 
that an algebra X of this monad is a bornological locally convex vector 
space endowed with operations which associate vectors \int f d\mu in X to 
incoming maps f : T --> X and measures \mu on T.  We prove that a Banach 
space is an M-algebra as soon as it has a Pettis integral for each 
incoming bounded weakly-measurable function.  It follows that all 
separable Banach spaces, and all reflexive Banach spaces, are M-algebras.




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