Hugo Dionizy Steinhaus – a Way to Contemporary Probability

Hugo Steinhaus (1887–1972) studied mathematics and philosophy at the Jan Kazimierz University in Lwow. Since 1905 he stayed in Göttingen where in 1911 he obtained his PhD under David Hilbert. In 1920 he became professor of the Lwow University. Together with Stefan Banach he established there a strong mathematical center for functional analysis. After the II World War he participated in creation of the mathematics department of the Wroclaw University and he was a founder of Wroclaw school for applied probability. He is the author and coauthor of 250 publications. In 1923 H. Steinhaus published in “Fundamenta Mathematicae” a study of Borel countable probabilities where, among other things, he gave an axiomatic definition of a probability measure on the space of countable zero‑one sequences. The goal of this note is to demonstrate a potentially important role of Steinhaus result in the process leading to final axiomatization of probability theory by Andrei Kolmogorov in 1933.