In order to investigate minimal sufficient conditions for an abstractintegral to belong to the convex hull of the integrand, we propose a system ofaxioms under which it happens. If the integrand is a continuous $R^n$-valuedfunction over a path connected topological space, we prove that any suchintegral can be represented as a convex combination of values of the integrandin at most $n$ points, which yields an ultimate multivariate mean valuetheorem.
展开▼
机译：为了研究抽象积分属于被积物的凸包的最小充分条件，我们提出了一个发生它的轴心系统。如果积分是在连接拓扑空间的路径上连续的$ R ^ n $值函数，我们证明任何这样的积分都可以表示为最多$ n $点的积分的值的凸组合，从而得出最终的多元均值价值定理。
展开▼
