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The n-dimensional deviation theorem and the magnitudes of the defining functions of the n-dimensional means

The linear ordering theorem for weighted means of functions relative to weight functions (Glaser, 2001) has several interesting implications similar to those of the one-dimensional Cashwell-Everett mean. (Cashwell-Everett, 1969). As an immediate consequence of the linear ordering theorem, we develop in this article the n-dimensional deviation theorem and a theorem dealing with inequalities related to the magnitudes of the defining functions of the n-dimensional means.

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