Geodesic
A categorical approach to integration
Theory and applications of categories, The Bourn Festschrift, Tome 23 (2010), pp. 243-250 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

Classification : 06E05 16A32, 18A15, 18A30, 18A35, 18A40, 18E05, 28A30, 28A33, 28A40, 28A45, 46G10
Keywords: internal Boolean algebra, universal measure, multiplicative measure, product measure, Boolean algebra of idempotents, symmetric monoidal closed category, cartesian closed category 
@article{TAC_2010_23_a11,
     author = {Reinhard B\"orger},
     title = {A categorical approach to integration},
     journal = {Theory and applications of categories},
     pages = {243--250},
     year = {2010},
     volume = {23},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2010_23_a11/}
}
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Reinhard Börger. A categorical approach to integration. Theory and applications of categories, The Bourn Festschrift, Tome 23 (2010), pp. 243-250. http://geodesic.mathdoc.fr/item/TAC_2010_23_a11/