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The Metrical Theory of Jacobi-Perron Algorithm

  • Book
  • © 1973

Overview

Authors:
  1. Fritz Schweiger
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 334)

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Table of contents (22 chapters)

  1. Front Matter

    Pages I-IV
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  2. Basic definitions

    • Fritz Schweiger
    Pages 1-8

  3. Cylinders

    • Fritz Schweiger
    Pages 8-15

  4. Increasing σ-fields

    • Fritz Schweiger
    Pages 15-17

  5. Conditional expectations

    • Fritz Schweiger
    Pages 17-21

  6. Ergodicity of the transformation

    • Fritz Schweiger
    Pages 22-23

  7. Existence of an equivalent invariant measure

    • Fritz Schweiger
    Pages 23-28

  8. The ergodic theorem

    • Fritz Schweiger
    Pages 28-34

  9. Kuzmin's Theorem

    • Fritz Schweiger
    Pages 34-42

  10. Convergence results

    • Fritz Schweiger
    Pages 42-49

  11. The Borel-Cantelli lemma of Schmidt-Philipp

    • Fritz Schweiger
    Pages 49-54

  12. Some extensions of Kuzmin's theorem

    • Fritz Schweiger
    Pages 54-56

  13. Outer measures

    • Fritz Schweiger
    Pages 56-60

  14. Hausdorff measures

    • Fritz Schweiger
    Pages 60-63

  15. Hausdorff dimension

    • Fritz Schweiger
    Pages 63-65

  16. Billingsley dimension

    • Fritz Schweiger
    Pages 65-68

  17. Comparison theorems

    • Fritz Schweiger
    Pages 68-75

  18. The main theorem of dimension theory of Jacobi algorithm

    • Fritz Schweiger
    Pages 75-90

  19. Ergodic invariant measures

    • Fritz Schweiger
    Pages 90-94

  20. Volume as approximation measure

    • Fritz Schweiger
    Pages 94-98
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Keywords

Bibliographic Information

  • Book Title: The Metrical Theory of Jacobi-Perron Algorithm

  • Authors: Fritz Schweiger

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0059845

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1973

  • Softcover ISBN: 978-3-540-06388-9Published: 27 July 1973

  • eBook ISBN: 978-3-540-47010-6Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 116

  • Topics: Mathematics, general

  • Industry Sectors: Engineering, IT & Software

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