Correlation Inequalities in Function Spaces

  • R. Ahlswede
  • V. Blinovsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)


We give a condition for a Borel measure on R [0,1] which is sufficient for the validity of an AD-type correlation inequality in the function space.


Probability Measure Function Space Distributive Lattice Equal Length Wiener Process 
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  1. 1.
    Ahlswede, R., Daykin, D.: An inequality for weights of two families of sets, their unions and intersections, Z. Wahrscheinlichkeitstheorie und verw. Gebiete 93, 183–185 (1979)Google Scholar
  2. 2.
    Karlin, S., Rinott, Y.: Classes of orderings of measures and related correlation inequalities, I. Multivariate Totally Positive Distributions, Journal of Multivariate Analysis 10, 467–498 (1980)MATHMathSciNetGoogle Scholar
  3. 3.
    Kemperman, J.: On the FKG inequality for measures in a partially ordered space. Indag. Math. 39, 313–331 (1977)MathSciNetGoogle Scholar
  4. 4.
    Birkhoff, G.: Lattice Theory, Providence, RI (1967)Google Scholar
  5. 5.
    Doob, J.: Stochastic Processes. Wiley, New York (1967)Google Scholar
  6. 6.
    Fortuin, C., Kasteleyn, P., Ginibre, J.: Correlation inequalities on some partially ordered sets. Comm. Math. Phys. 22, 89–103 (1971)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Holley, R.: Remarks on the FKG inequalities. Comm. Math. Phys. 36, 227–231 (1974)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Preston, C.: A generalization of the FKG inequalities. Comm. Math. Phys. 36, 233–241 (1974)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • R. Ahlswede
    • 1
  • V. Blinovsky
    • 2
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2.Russian Academy of Sciences Institute of Problems of Information TransmissionMoscowRussia

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