A law of large numbers for abstract random variables

Summary It was emphasized by Fréchet [8] that in many of the practical applications, we get, as a result of a random experiment, an abstract random variableX belonging to a setX. Givenn determinations of the variableX, an arithmetic meanZ _n is introduced in 2-. It reduces to the classical arithmetic mean, whenX is the set of real numbers. Moreover, if the random variableX is Gaussian, having a meanM(X), and belongs to a certain (4-) familyF, the introduced arithmetic meanZ _n constitutes an exhausting estimation [5] of the meanM(X).