Algebraic theory of vector-valued integration

@article{LucyshynWright2012AlgebraicTO,
  title={Algebraic theory of vector-valued integration},
  author={R. B. Lucyshyn-Wright},
  journal={Advances in Mathematics},
  year={2012},
  volume={230},
  pages={552-576}
}
  • R. B. Lucyshyn-Wright
  • Published 2012
  • Mathematics
  • Advances in Mathematics
  • 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 that associate vectors ∫fdμ in X to incoming maps f:T→X and measures μ 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… CONTINUE READING
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