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Mathematics > Functional Analysis

arXiv:0710.2614 (math)
[Submitted on 13 Oct 2007]

Title:Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables

Authors:Jean-Luc Marichal
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Abstract: 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.
Comments: 15 pages
Subjects: Functional Analysis (math.FA); Probability (math.PR)
MSC classes: 26B10, 26B20 (Primary) 60A10 (Secondary)
Cite as: arXiv:0710.2614 [math.FA]
  (or arXiv:0710.2614v1 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.0710.2614
Journal reference: Journal of Mathematical Analysis and Applications 341 (1) (2008) 200-210
Related DOI: https://doi.org/10.1016/j.jmaa.2007.10.021

Submission history

From: Jean-Luc Marichal [view email]
[v1] Sat, 13 Oct 2007 15:13:50 UTC (10 KB)
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