In ergodic theory, Kac's lemma, demonstrated by mathematician Mark Kac in 1947,[1] is a lemma stating that in a measure space the orbit of almost all the points contained in a set of such space, whose measure is , return to within an average time inversely proportional to .[2]
The lemma extends what is stated by Poincaré recurrence theorem, in which it is shown that the points return in infinite times.[3]