  In neuroscience, the time elapsed since the last discharge has been used to
predict the probability of the next discharge. Such predictions can be improved
taking into account the last two discharge times, and possibly more. Such
multi-time processes arise in many other areas and there is no universal
limitation on the number of times to be used. This observation leads us to
study the infinite-times renewal equation as a simple model to understand the
meaning and properties of such partial differential equations depending on an
infinite number of variables.We define two notions of solutions, prove
existence and uniqueness of solutions, possibly measures. We also prove the
long time convergence, with exponential rate, to the steady state in different,
strong or weak, topologies depending on assumptions on the coefficients.
