Advertisement

The Mathematical Intelligencer

, Volume 4, Issue 3, pp 146–157 | Cite as

About book

  • Peter G. Bergmann
Article
  • 48 Downloads

Keywords

Ising Model Markov Random Field Median Graph Perfect Measure Compact Class 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. H. Fremlin: Pointwise compact sets of measurable functions. Manuscripta Math. 15 (1975), 219–242CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    R. F. Geitz: Pettis integration. Proc. Amer. Math. Soc. 82 (1981), 81–86CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    E. Marczewski: On compact measures. Fund. Math. 40 (1953), 113–124zbMATHMathSciNetGoogle Scholar
  4. 4.
    E. Marczewski, R. Sikorski: Measures on nonseparable metric spaces: Colloq. Math. 1 (1948), 133–139zbMATHMathSciNetGoogle Scholar
  5. 5.
    K. Musial: Projective limits of perfect measure spaces. Fund. Math. 110 (1980), 163–189zbMATHMathSciNetGoogle Scholar
  6. 6.
    J. K. Pachi: Disintegration and compact measures. Math. Scand. 43 (1978), 157–168MathSciNetGoogle Scholar
  7. 7.
    C. Ryll-Nardzewski: On quasi-compact measures. Fund. Math. 40(1953), 125–130MathSciNetGoogle Scholar

References

  1. 1.
    Averintsev, M. B.: On a method of describing discrete parameter random fields.Problemy Peredacki Informatsii 6, 100–109 (1970)Google Scholar
  2. 2.
    Dobrushin, R. L.: The description of a random field by means of conditional probabilities and conditions of its regularity.Theor. Probi. Appl. 13, 197–224 (1968)CrossRefGoogle Scholar
  3. 3.
    Dobrushin, R. L.: The problem of uniqueness of a Gibbsian random field and the problem of phase transitions.Functional Anal. Appl. 2, 302–312 (1968)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dynkin, E. B.: Markov processes and random fields.Bull. A.M.S. 3, 975–1000 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Gallavotti, G., Jona-Lasinio, G.: Limit theorems for multidimensional Markov processes.Commun. Math. Phys. 41, 301–307 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Jona-Lasinio, G.: The renormalization group: A probabilistic view.llNuovo Cimento 26B, 99–119 (1975)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Nelson, E.: Construction of quantum fields from Markov fields.J. Functional Anal. 12, 97–112 (1973)CrossRefzbMATHGoogle Scholar
  8. 8.
    Niemeyer, Th., Van Leeuwen, J. M. J.: Wilson theory for two dimensional Ising spin system.Physica 71, 17–40 (1974)CrossRefGoogle Scholar
  9. 9.
    Preston, C. J.: Gibbs States on Countable Sets, Cambridge University Press (1974)Google Scholar
  10. 10.
    Rozanov, Ju. A.: Markov random fields and stochastic partial differential equations.Math USSR Sbomik 32, 515–534 (1977)CrossRefzbMATHGoogle Scholar
  11. 11.
    Spitzer, F.: Markov random fields and Gibbs ensembles.Am. Math. Monthly 78, 142–154 (1971)CrossRefzbMATHMathSciNetGoogle Scholar

References

  1. 1.
    E. J. Wilczynski:Transactions of the American Mathematical Society, v. 21, pp. 157–206 (1920). See also references cited here to earlier papersCrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    D. E. Richmond, “Calculus, A New Look,”American Mathe matical Monthly, v. 70, pp. 415–423 (1963)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Albert G. Fadell:Calculus with analytic geometry, pp. 68-73, Van Nostrana (1964)Google Scholar
  4. 4.
    Blanche Descartes: Book Review of“Graph theory with applications, “ by J. A. Bondy and U. S. R. Murty, American Elsevier Publishing Co., Inc., 1976, which appeared in theBulletin of the American Mathematical Society, vol. 83, pp. 313–315 (1977)CrossRefMathSciNetGoogle Scholar
  5. 5.
    John R. Isbell: Letter to the Editor,Notices of the American Mathematical Society, vol. 24, pp. 372–373 (October 1977)Google Scholar
  6. 6.
    R. E. Greenwood, A. M. Gleason: Combinational Relations and Chromatic Graphs.Canadian Journal of Mathematics, vol. 7, pp. 1–7 (1955)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 1982

Authors and Affiliations

  • Peter G. Bergmann
    • 1
  1. 1.Department of PhysicsSyracuseUSA

Personalised recommendations