High Quality Content by WIKIPEDIA articles! The Turan–Kubilius inequality is a mathematical theorem in probabilistic number theory. It is useful for proving results about the normal order of an arithmetic function. :305–308 The theorem was proved in a special case in 1934 by Paul Turan and generalized in 1956 and 1964 by Jonas Kubilius. Turan developed the inequality to create a simpler proof of the Hardy–Ramanujan theorem about the normal order of the number (n) of distinct prime divisors of an integer n.:316 There is an exposition of Turan's proof in Hardy

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