| Abstract
| - Abstract. In the present note we completely solve the characterization problem of quasiarithmetic means with weight function, that is, functions of the form$$M(x_1 ,...,x_n ) = f^{ - 1} \left( {\sum\limits_{i = 1}^n {p(x_i )} f(x_i )/\sum\limits_{i = 1}^n {p(x_i )} } \right)$$ (f is a strictly monotonic continuous real function andp is a positive valued real function.) The result obtained gives a partial answer to a 22-year-old problem of Aczél [1] and generalizes the characterization theorem of quasiarithmetic means which is due to Kolmogorov [8], Nagumo [9] and de Finetti [7].
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