On the inequalities of Erdős-Turán and Berry-Esseen. I (Q1118645)
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scientific article; zbMATH DE number 4095609
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the inequalities of Erdős-Turán and Berry-Esseen. I |
scientific article; zbMATH DE number 4095609 |
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On the inequalities of Erdős-Turán and Berry-Esseen. I (English)
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1988
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This note contains the announcement of various generalizations and improvements of the Erdős-Turán and Berry-Esseen inequalities for distances of distribution functions. The new ingredient is the use of the modulus of nonmonotonicity instead of the modulus of continuity. Several earlier inequalities such as those of \textit{A. S. Fajnlejb} [Izv. Akad. Nauk SSSR, Ser. Mat. 32, 859-879 (1968; Zbl 0164.055)] and of the reviewer and \textit{W. Philipp} [Duke Math. J. 40, 633-649 (1973; Zbl 0273.10043)] are subsumed in the present results.
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uniform distribution mod 1
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closeness
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upper bounds
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supremum norm
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modulus of nonmonotonicity
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Erdős-Turán inequality
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Berry-Esseen inequality
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