Axiomatics for the mean using Bemporad’s condition. (English) Zbl 1331.60008
Summary: Joining previous authors, we propose axiomatic properties that yield the mean as the unique measure of center of a data set. In addition to familiar properties such as symmetry, homogeneity, and translativity, we make use of a condensation principle, first considered by G. Bemporad [Atti Accad. Naz. Lincei, Rend., VI. Ser. 3, 87–91 (1926; JFM 52.0079.03)], that ties together means for different sample sizes and identifies an important physical characteristic of the center of mass of a body.
MSC:
| 60A05 | Axioms; other general questions in probability |
| 26E60 | Means |
| 39B22 | Functional equations for real functions |
Citations:
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