  In this paper two hypotheses are developed. The first hypothesis is the
existence of random phenomena/experiments in which the events cannot generally
be assigned a definite probability but that nevertheless admit a class of
nearly certain events. These experiments are referred to as
\textit{typicalistic} (instead of probabilistic) experiments. As probabilistic
experiments are represented by probability spaces, typicalistic experiments can
be represented by \textit{typicality spaces}, where a typicality space is
basically a probability space in which the probability measure has been
replaced by a much less structured typicality measure $T$. The condition $T(A)
\approx 1$ defines the typical sets, and a typicality space is related to a
typicalistic experiment by associating the typical sets of the former with the
nearly certain events of the latter. Some elements of a theory of typicality,
including the definition of typicality spaces, are developed in the first part
of the paper. The second hypothesis is that the evolution of a quantum particle
(or of a system of quantum particles) can be considered a typicalistic
phenomenon, so that it can be represented by the combination of typicality
theory and quantum mechanics. The result is a novel formulation of quantum
mechanics that does not present the measurement problem and that could be a
viable alternative to Bohmian mechanics. This subject is developed in the
second part of the paper.
