A Central Limit Theorem and a Strong Mixing Condition

* research for this paper was supported by the United States Air Force under Contract No. AF18(600-685) monitored by the Office of Scientific Research. 1 A discussion of the problem along with the necessary references will be found in Harry Pollard, The Harmonic Analysis of Bounded Functions, Duke Math. / . , 20, 499-512, 1953. 2 See ibid. 3 See S. Bochner, Fouriersche Integrate (Leipzig, 1932), p. 33. 4 Levitan polynomial. See N.I. Achieser, Approximationstheorie (Berlin, 1953), p. 146.