ABSTRACT
The Hardy, Littlewood, Polya class of power means (wiza 1 + …+wn za n)1/a, including the usual harmonic, geometric, and arithmetic mean values, has been generalized by Bruno deFinetti and B. C. Carlson. These two generalizations are here simultaneously extended to a comprehensive generalized mean value involving an arbitrary continuous strictly monotonic function and a linear form in the data values with Dirichlet-distributed coefficients. Properties are given which relate the new mean naturally to its deFinetti and Carlson subclasses. Statistical interpretations and possible further extensions arc discussed.