Equivalent-singular dichotomy for quasi-invariant ergodic measures

Yoshiaki Okazaki

Annales de l'I.H.P. Probabilités et statistiques (1985)

  • Volume: 21, Issue: 4, page 393-400
  • ISSN: 0246-0203

How to cite

top

Okazaki, Yoshiaki. "Equivalent-singular dichotomy for quasi-invariant ergodic measures." Annales de l'I.H.P. Probabilités et statistiques 21.4 (1985): 393-400. <http://eudml.org/doc/77265>.

@article{Okazaki1985,
author = {Okazaki, Yoshiaki},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {locally convex vector spaces; Hájek-Feldman’s dichotomy; Fernique's dichotomy; symmetric stable distributions; equivalent-singular dichotomy},
language = {eng},
number = {4},
pages = {393-400},
publisher = {Gauthier-Villars},
title = {Equivalent-singular dichotomy for quasi-invariant ergodic measures},
url = {http://eudml.org/doc/77265},
volume = {21},
year = {1985},
}

TY - JOUR
AU - Okazaki, Yoshiaki
TI - Equivalent-singular dichotomy for quasi-invariant ergodic measures
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1985
PB - Gauthier-Villars
VL - 21
IS - 4
SP - 393
EP - 400
LA - eng
KW - locally convex vector spaces; Hájek-Feldman’s dichotomy; Fernique's dichotomy; symmetric stable distributions; equivalent-singular dichotomy
UR - http://eudml.org/doc/77265
ER -

References

top
  1. [1] S.D. Chatterji and S. Ramaswamy, Mesures gaussiennes et mesures produits. Springer-Verlag, Lecture Notes in Math., t. 920, 1982, p. 570-580. Zbl0504.28017MR658715
  2. [2] J. Feldman, Equivalence and perpendicularity of Gaussian Processes. Pacific J. Math., t. 8, 1958, p. 699-708. Zbl0084.13001MR102760
  3. [3] X. Fernique, Comparaison de mesures gaussiennes et de mesures produits. Ann. Inst. H. Poincaré, t. 20, 1985, p. 165-175. Zbl0536.60047MR749622
  4. [4] J. Hajek, On a property of normal distributions of any stochastic processes. Selected translations in Math. Statis. Prob., t. 1, 1958-1961, p. 245-252. Zbl0112.09702MR116379
  5. [5] E. Hewitt and K.A. Ross, Abstract harmonic analysis. Die Grundlehren der Math. Wiss., t. 115, Springer-Verlag, 1963. Zbl0115.10603
  6. [6] K. Ito and M. Nisio, On the convergence of sums of independent random variables. Osaka J. Math., t. 5, 1968, p. 35-48. Zbl0177.45102MR235593
  7. [7] A. Janssen, A survey about zero-one laws for probability measures on linear spaces and locally compact groups. Springer-Verlag, Lecture Notes in Math., t. 1064, 1984, p. 551-563. Zbl0542.60036MR772429
  8. [8] S. Kakutani, On equivalence of infinite product measures. Ann. of Math., t. 49, 1948, p. 214-224. Zbl0030.02303MR23331
  9. [9] M. Kanter, Equivalence singularity dichotomies for a class of ergodic measures. Math. Proc. Camb. Phil. Soc., t. 81, 1977, p. 249-252. Zbl0383.60041MR436306
  10. [10] J. Von Neumann, Uber einen Satz von Herrn M. H. Stone. Ann. of Math., t. 33, 1932, p. 567-573. Zbl0005.16402MR1503076JFM58.0423.03
  11. [11] Ju A. Rozanov, Infinite-dimensional Gaussian distributions. Proc. Steklov Inst. Math., t. 108, 1968, A. M. S. (English translation). Zbl0245.60036MR298752
  12. [12] H. Sato and Y. Okazaki, Separabilities of a Gaussian Radon measure. Ann. Inst. H. Poincaré, t. 11, 1975, p. 287-298. Zbl0362.60015MR400323
  13. [13] A.V. Skorohod, Integration in Hilbert space. Ergebnisse der Math., t. 79, Springer-Verlag, 1974. Zbl0307.28010MR466482
  14. [14] A. Tortrat, Lois e(λ) dans les espaces vectoriels et lois stables. Z. Wahrscheinlichkeitstheorie verw., t. 37, 1976, p. 175-182. Zbl0335.60013MR428371
  15. [15] J. Zinn, Zero-one laws for non-Gaussian measures. Proc. of A. M. S., t. 44, 1974, p. 179-185. Zbl0309.60022MR345158

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.