Strongly consistent estimates are shown, via relative frequency, for the
probability of "white balls" inside a dichotomous urn when such a probability
is an arbitrary continuous time dependent function over a bounded time
interval. The asymptotic behaviour of relative frequency is studied in a
nonstationary context using a Riemann-Dini type theorem for SLLN of random
variables with arbitrarily different expectations; furthermore the theoretical
results concerning the SLLN can be applied for estimating the mean function of
unknown form of a general nonstationary process.Comment: 29 page
