Preprint: A general Fubini theorem for the Riesz paradigm
A preprint of my paper "A general Fubini theorem for the Riesz paradigm" is available at http://arxiv.org/abs/1210.4542 This paper includes results presented at the Workshop on Category Theory, Coimbra, July 2012. An abstract is included below. Your comments are welcome. Other papers of mine are available through my website, including "Algebraic theory of vector-valued integration" (published in Advances in Mathematics, June 2012) and "Totally distributive toposes" (published in Journal of Pure and Applied Algebra, November 2012 issue). http://www.math.yorku.ca/~rorylw/ Regards, Rory Lucyshyn-Wright Abstract: We prove an abstract Fubini-type theorem in the context of monoidal and enriched category theory, and as a corollary we establish a Fubini theorem for integrals on arbitrary convergence spaces that generalizes (and entails) the classical Fubini theorem for Radon measures on compact Hausdorff spaces. Given a symmetric monoidal closed adjunction satisfying certain hypotheses, we show that an associated monad of natural distributions D is commutative. Applying this result to the monoidal adjunction between convergence spaces and convergence vector spaces, the commutativity of D amounts to a Fubini theorem for continuous linear functionals on the space of scalar functions on an arbitrary convergence space. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (1)
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Rory Lucyshyn-Wright