An axiomatic integral and a multivariate mean value theorem
| Autor: | Milan Merkle |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Convex hull
Physics::Computational Physics Pure mathematics Multivariate statistics Applied Mathematics Mathematical analysis Probability (math.PR) Order (ring theory) Function (mathematics) Topological space Mean value theorem (divided differences) FOS: Mathematics Discrete Mathematics and Combinatorics Convex combination 28A30 26E60 26B25 Axiom Mathematics - Probability Analysis Mathematics |
| DOI: | 10.48550/arxiv.1506.05551 |
| Popis: | 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 $\mathbf {R}^{n}$ -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 n points, which yields an ultimate multivariate mean value theorem. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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