Description
The theory of quasi-arithmetic means developed in the 1930s, Kolmogorov's characterization theorem, has inspired numerous generalizations and researches in the last nearly one hundred years. In the 1950s, Bajraktarević and in the 1970s, Daróczy introduced central concepts that have been the focus of research ever since. The problems of equality, homogeneity, comparison and characterization were completely solved, and the methods were even applied to more general middle classes. Serious partial results were also achieved in the solution of the so-called invariance equation. The presentation provides an overview of these, and also presents the information theory, decision theory and probability calculation applications of the results.