Corpus ID: 118900951

Riesz-Schwartz extensive quantities and vector-valued integration in closed categories

@article{LucyshynWright2013RieszSchwartzEQ,
  title={Riesz-Schwartz extensive quantities and vector-valued integration in closed categories},
  author={R. B. Lucyshyn-Wright},
  journal={arXiv: Functional Analysis},
  year={2013}
}
  • R. B. Lucyshyn-Wright
  • Published 2013
  • Mathematics
  • arXiv: Functional Analysis
  • We develop aspects of functional analysis in an abstract axiomatic setting, through monoidal and enriched category theory. We work in a given closed category, whose objects we call spaces, and we study R-module objects therein (or algebras of a commutative monad), which we call linear spaces. Building on ideas of Lawvere and Kock, we study functionals on the space of scalar-valued maps, including compactly-supported Radon measures and Schwartz distributions. We develop an abstract theory of… CONTINUE READING
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