On generalized variations (II)
R. Leśniewicz, W. Orlicz (1973)
Studia Mathematica
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R. Leśniewicz, W. Orlicz (1973)
Studia Mathematica
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L Carlitz (1962)
Acta Arithmetica
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von Neumann, John (1942)
Portugaliae mathematica
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D. Grubb, Charles Moore (1994)
Studia Mathematica
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Let the coefficients of a lacunary cosine series be bounded and not square-summable. Then the partial sums of the series are recurrent.
Stanisław Knapowski, W Staś (1962)
Acta Arithmetica
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L. Włodarski (1961)
Annales Polonici Mathematici
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Stanisław Knapowski (1962)
Acta Arithmetica
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S. Uchiyama (1972)
Acta Arithmetica
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L Carlitz (1962)
Acta Arithmetica
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Rafał Latała (1996)
Studia Mathematica
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Let be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable , where are vectors of some Banach space. We derive approximate formulas for the tail and moments of ∥X∥. The estimates are exact up to some universal constant and they extend results of S. J. Dilworth and S. J. Montgomery-Smith [1] for the Rademacher sequence and E. D. Gluskin and S. Kwapień [2] for real coefficients.