An axiomatic integral and a multivariate mean value theorem
Probability
2015-06-19 v1
Abstract
In order to investigate minimal sufficient conditions for an abstract integral to belong to the convex hull of the integrand, we propose a system of axioms under which it happens. If the integrand is a continuous -valued function over a path connected topological space, we prove that any such integral can be represented as a convex combination of values of the integrand in at most points, which yields an ultimate multivariate mean value theorem.
Cite
@article{arxiv.1506.05551,
title = {An axiomatic integral and a multivariate mean value theorem},
author = {Milan Merkle},
journal= {arXiv preprint arXiv:1506.05551},
year = {2015}
}