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181   $ctxt
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183   $acr
200 10$aMixing sequences of random variables and probabilistic number theory /$fby Walter Philipp
210  1$aProvidence :$cAmerican Mathematical Society,$d1971.
215   $a1 online resource (108 p.)
225 1 $aMemoirs of the American Mathematical Society ;$vnumber 114
300   $aCover title.
311   $a0-8218-1814-7 
320   $aIncludes bibliographical references.
327   $a""Contents""; ""Introduction""; ""1. Limit theorems for mixing sequences of random variables""; ""1.1. The central problem""; ""1.2. The central limit theorem with remainder and the law of the iterated logarithm""; ""1.3. An extension of the law of the iterated logarithm""; ""1.3.1. The upper bound""; ""1.3.2. The lower bound""; ""2. Limit theorems for continued fractions and related algorithms""; ""3. Limit theorems in Diophantine approximation""; ""3.1. Introduction""; ""3.2. Preliminaries""; ""3.3. The asymptotic behavior of N*""; ""3.3.1. Preparatory remarks""
327   $a""3.3.2. The law of the iterated logarithm and the central limit theorem for the y[sub(j)]'s and the z[sub(j)]'s""""3.3.3. Proof of Theorem 3.1.2*""; ""3.3.4. Proof of Theorem 3.1.1*""; ""3.4. The asymptotic behavior of N""; ""4. The law of the iterated logarithm for discrepancies of sequences uniformly distributed mod 1""; ""4.1. The discrepancies of almost all sequences (in the sense of the infinite product measure)""; ""4.2. The discrepancies of sequences of the type ""; ""5. The distribution of additive functions""; ""5.1. Kubiliusf fundamental lemma""
327   $a""5.2. Preparatory lemmas""""5.3. Limit theorems for additive functions of class H""; ""5.4. A more direct method""; ""5.5. A result on uniform distribution""; ""References""
410  0$aMemoirs of the American Mathematical Society ;$vnumber 114.
606   $aProbabilistic number theory
606   $aSequences (Mathematics)
606   $aRandom variables
615  0$aProbabilistic number theory.
615  0$aSequences (Mathematics)
615  0$aRandom variables.
676   $a512/.7
700   $aPhilipp$b Walter$f1936-$01632946
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910828803403321
996   $aMixing sequences of random variables and probabilistic number theory$93972429
997   $aUNINA