Skip to main content

Generalized martingales

Part of the Lecture Notes in Mathematics book series (LNM,volume 160)

Keywords

  • Measure Space
  • Ergodic Theorem
  • Orlicz Space
  • Convergence Theory
  • Banach Function Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. A. Akcoglu and R. V. Chacón, "A convexity theorem for positive operators", Z. Wahrscheinlichkeitstheorie verw. Geb., 3(1965), 328–332.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. G. Bray, "Théorèmes ergodiques de convergence en moyenne", J. Math. Anal. Applic., 25(1969), 471–502.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. E. Briem, A. Guichardet et Nguyen-Xuan-Loc, "Les martingales généralisées", C.R. Acad. Sci., Ser. A, 270(1970), 373–375.

    MathSciNet  MATH  Google Scholar 

  4. Y. S. Chow, "Martingales in a σ-finite measure space indexed by directed sets", Trans. Amer. Math. Soc., 97(1960), 254–285.

    MathSciNet  MATH  Google Scholar 

  5. N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Interscience, New York, 1958.

    MATH  Google Scholar 

  6. N. E. Gretsky, "Representation theorems on Banach function spaces", Amer. Math. Soc. Memoirs #84(1968), 52 pp.

    Google Scholar 

  7. P. R. Halmos, Lectures on Ergodic Theory, Publication of the Math. Soc. Japan #3(1956).

    Google Scholar 

  8. E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Pub. #31(1957).

    Google Scholar 

  9. A. Ionescu Tulcea and C. Ionescu Tulcea, "Abstract ergodic theorems", Trans. Amer. Math. Soc., 107(1963), 107–124.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. M. Jerison, "Martingale formulation of ergodic theorems", Proc. Amer. Math. Soc., 10(1959), 531–539.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. U. Krengel, "A local ergodic theorem", Invent. Math., 6(1969), 324–333.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. W.A.J. Luxemburg and A. C. Zaanen, "Compactness of integral operators in Banach function spaces", Math. Ann., 149(1963), 150–180.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. M. M. Rao, "Linear functionals on Orlicz spaces", Nieuw Arkiv v. Wisk (3), 12(1964), 77–98.

    MathSciNet  MATH  Google Scholar 

  14. M. M. Rao, "Interpolation, ergodicity, and martingales", J. Math. Mech., 16(1966), 543–568.

    MathSciNet  MATH  Google Scholar 

  15. M. M. Rao, "Stone-Weierstrass theorems for function spaces", J. Math. Anal. Applic., 25(1969), 362–371.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. M. M. Rao, "Contractive projections and prediction operators", Bull. Amer. Math. Soc., 75(1969), 1369–1373.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. M. M. Rao, "Operateurs de moyennes et moyennes conditionnelles", C.R. Acad. Sci., Ser. A, 268(1969), 795–797.

    MathSciNet  MATH  Google Scholar 

  18. M. M. Rao, "Inference in stochastic processes-IV", (to appear).

    Google Scholar 

  19. M. M. Rao, "Conditional expectations, Reynold's operators, and vector measures", Bull. Amer. Math. Soc., 76(1970), (to appear).

    Google Scholar 

  20. G.-C. Rota, "Une théorie unifiée des martingales et des moyennes ergodiques", C.R. Acad. Sci., Ser. A, 252(1961), 2064–2066.

    MathSciNet  MATH  Google Scholar 

  21. G.-C. Rota, "On the maximal ergodic theorem for Abel-limits", Proc. Amer. Math. Soc., 14(1963), 722–723.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. G.-C. Rota, "Reynold's operators", Proc. Symp. Appl. Math., Amer. Math. Soc., 16(1964), 70–83.

    CrossRef  MathSciNet  Google Scholar 

  23. A. E. Taylor, Introduction to Functional Analysis, Wiley, New York, 1958.

    MATH  Google Scholar 

  24. J. J. Uhl, Jr., "Orlicz spaces of finitely additive set functions", Studia Math., 29(1967), 19–58.

    MathSciNet  MATH  Google Scholar 

  25. A. C. Zaanen, Integration, North-Holland Publishing Company, 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1970 Springer-Verleg

About this paper

Cite this paper

Rao, M.M. (1970). Generalized martingales. In: Contributions to Ergodic Theory and Probability. Lecture Notes in Mathematics, vol 160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060657

Download citation

  • DOI: https://doi.org/10.1007/BFb0060657

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05188-6

  • Online ISBN: 978-3-540-36371-2

  • eBook Packages: Springer Book Archive