  The consistency of the Aalen--Johansen-derived estimator of state occupation
probabilities in non-Markov multi-state settings is studied and established via
a new route. This new route is based on interval functions and relies on a
close connection between additive and multiplicative transforms of interval
functions, which is established. Under certain assumptions, the consistency
follows from explicit expressions of the additive and multiplicative transforms
related to the transition probabilities as interval functions, which are
obtained, in combination with certain censoring and positivity assumptions.
