03057nam 2200577 450 991078861300332120170918214639.00-8218-9911-2(CKB)3360000000464028(EBL)3113704(SSID)ssj0000973345(PQKBManifestationID)11527851(PQKBTitleCode)TC0000973345(PQKBWorkID)10959421(PQKB)10391246(MiAaPQ)EBC3113704(RPAM)3162588(PPN)195409981(EXLCZ)99336000000046402820711015d1971 uy| 0engur|n|---|||||txtccrMixing sequences of random variables and probabilistic number theory /by Walter PhilippProvidence :American Mathematical Society,1971.1 online resource (108 p.)Memoirs of the American Mathematical Society ;number 114Cover title.0-8218-1814-7 Includes bibliographical references.""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""""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""""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""Memoirs of the American Mathematical Society ;number 114.Probabilistic number theorySequences (Mathematics)Random variablesProbabilistic number theory.Sequences (Mathematics)Random variables.512/.7Philipp Walter1936-1542969MiAaPQMiAaPQMiAaPQBOOK9910788613003321Mixing sequences of random variables and probabilistic number theory3796177UNINA