These three conditions are certainly necessary for P.A/ to be a probability. It
was the achievement of Kolmogorov to show that these three requirements allow a
complete and consistent definition of such an assignment for all events.
Note that we have introduced probability without saying what it means, i.e.,
how to measure it. We have merely introduced an assignment which has all
properties one would expect of the notion of probability. In Part II we will deal
with the measurement of probabilities and of quantities which are calculated from
probabilities.