#
A categorical approach to integration

##
Reinhard Börger

We present a general treatment of measures and integrals in
certain (monoidal closed) categories. Under appropriate conditions
the integral can be defined by a universal property, and the
universal measure is at the same time a universal multiplicative
measure. In the multiplicative case this assignment is right
adjoint to the formation of the Boolean algebra of idempotents.
Now coproduct preservation yields an approach to product measures.

Keywords:
internal Boolean
algebra, universal measure, multiplicative measure, product
measure, Boolean algebra of idempotents, symmetric monoidal
closed category, cartesian closed category

2000 MSC:
06E05 16A32, 18A15, 18A30,
18A35, 18A40, 18E05, 28A30, 28A33, 28A40, 28A45, 46G10

*Theory and Applications of Categories,*
Vol. 23, 2010,
No. 12, pp 243-250.

http://www.tac.mta.ca/tac/volumes/23/12/23-12.dvi

http://www.tac.mta.ca/tac/volumes/23/12/23-12.ps

http://www.tac.mta.ca/tac/volumes/23/12/23-12.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/23/12/23-12.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/23/12/23-12.ps

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