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  • © 1973

The Metrical Theory of Jacobi-Perron Algorithm

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 334)

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  • ISBN: 978-3-540-47010-6
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Table of contents (22 chapters)

  1. Front Matter

    Pages I-IV
  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. Ergodic invariant measures

    • Fritz Schweiger
    Pages 90-94
  19. Volume as approximation measure

    • Fritz Schweiger
    Pages 94-98

Keywords

  • Algorithm
  • Invariant
  • Jacobi-Perronscher Algorithmus
  • Mass (Math.)
  • proof
  • theorem

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: 978-3-540-06388-9

  • eBook ISBN: 978-3-540-47010-6

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 116

  • Topics: Mathematics

Buying options

eBook USD 29.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-47010-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 39.95
Price excludes VAT (USA)