显式依赖于变量最小值和最大值的函数的多元积分
Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables
摘要：
利用多重积分的一些基本演算，我们给出了积分$$ \int_{]a,b[^n} f(\mathbf{x},\min x_i,\max x_i) d\mathbf{x}, $$的另一种表达式，其中最小值和最大值用两个单变量代替。我们证明了有用的表达在计算的Orness和andness平均值的某些聚合函数。通过将所得结果推广到黎曼-斯蒂尔切斯积分，我们还提供了计算某些期望值和分布函数的方法.
英文摘要：
By using some basic calculus of multiple integration, we provide an alternative expression of the integral $$ \int_{]a,b[^n} f(\mathbf{x},\min x_i,\max x_i) d\mathbf{x}, $$ in which the minimum and the maximum are replaced with two single variables. We demonstrate the usefulness of that expression in the computation of orness and andness average values of certain aggregation functions. By generalizing our result to Riemann-Stieltjes integrals, we also provide a method for the calculation of certain expected values and distribution functions.
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