02504nam 2200613 450 99646664800331620220819141730.03-540-47010-710.1007/BFb0059845(CKB)1000000000438463(SSID)ssj0000324815(PQKBManifestationID)12064900(PQKBTitleCode)TC0000324815(PQKBWorkID)10320817(PQKB)11619302(DE-He213)978-3-540-47010-6(MiAaPQ)EBC5610996(Au-PeEL)EBL5610996(OCoLC)1078997173(MiAaPQ)EBC6812424(Au-PeEL)EBL6812424(OCoLC)1112967113(PPN)155216007(EXLCZ)99100000000043846320220819d1973 uy 0engurnn|008mamaatxtccrThe metrical theory of Jacobi-Perron algorithm /Fritz Schweiger1st ed. 1973.Berlin ;Heidelberg :Springer-Verlag,1973.1 online resource (VIII, 116 p.) Lecture Notes in Mathematics ;Volume 334Bibliographic Level Mode of Issuance: Monograph3-540-06388-9 Basic definitions -- Cylinders -- Increasing ?-fields -- Conditional expectations -- Ergodicity of the transformation -- Existence of an equivalent invariant measure -- The ergodic theorem -- Kuzmin's Theorem -- Convergence results -- The Borel-Cantelli lemma of Schmidt-Philipp -- Some extensions of Kuzmin's theorem -- Outer measures -- Hausdorff measures -- Hausdorff dimension -- Billingsley dimension -- Comparison theorems -- The main theorem of dimension theory of Jacobi algorithm -- Ergodic invariant measures -- Volume as approximation measure -- Proof of the conjecture for n=1 and n=2 -- The metrical theory of Jacobi-Perron algorithm -- Errata.Lecture notes in mathematics (Springer-Verlag) ;Volume 334.Jacobi polynomialsAlgorithmsComputer algorithmsErgodic theoryJacobi polynomials.AlgorithmsComputer algorithms.Ergodic theory.515.55Schweiger Fritz441282MiAaPQMiAaPQMiAaPQBOOK996466648003316Metrical theory of Jacobi-Perron algorithm81429UNISA