The occurrence times of a measurable set "A" is defined as the set "k"1, "k"2, "k"3, ..., of times "k" such that "Tk"("x") is in "A", sorted in increasing order. The differences between consecutive occurrence times "Ri" = "ki" − "k""i"−1 are called the recurrence times of "A". Another consequence of the ergodic theorem is that the average recurrence time of "A" is inversely proportional to the measure of "A", assuming that the initial point "x" is in "A", so that "k"0 = 0.