Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 5 (2000) > Paper 11 open journal systems 


Strict Fine Maxima

P. J. Fitzsimmons, University of California, San Diego


Abstract
We provide a simple probabilistic proof of a result of J. Král and I. Netuka: If  f  is a measurable real-valued function on Rd (d> 1) then the set of points at which  f  has a strict fine local maximum value is polar.


Full text: PDF

Pages: 91-94

Published on: June 15, 2000


Bibliography
  1. A. Ancona: Sur une conjecture concernant la capacité et l'effilement. Lecture Notes in Math. 1096, Théorie du potentiel (Orsay, 1983), pp. 34--68. Springer-Verlag, Berlin-New York, 1984. MR 88f:31006
  2. K. L. Chung: Probabilistic approach in potential theory to the equilibrium problem. Ann. Inst. Fourier (Grenoble) 23 (1973) 313--322. MR 52 #12098
  3. C. Dellacherie and P.-A. Meyer: Probabilités et potentiel, Chapitres V à VIII, Théorie des martingales. Hermann, Paris, 1980. MR 82b:60001
  4. P. J. Fitzsimmons: Homogeneous random measures and a weak order for the excessive measures of a Markov process. Trans. Amer. Math. Soc. 303 (1987) 431--478. MR 89c:60088
  5. R. K. Getoor and M. J. Sharpe: Last exit times and additive functionals. Ann. Probability 1 (1973) 550--569. MR 50 #5951
  6. M. Fukushima, Y. Oshima and M. Takeda: Dirichlet forms and symmetric Markov processes. Walter de Gruyter & Co., Berlin, 1994. MR 96f:60126
  7. J. Král and I. Netuka: Fine topology in potential theory and strict maxima of functions. Exposition. Math. 5 (1987) 185--191. MR 88d:31007
  8. H. P. McKean, Jr.: A probabilistic interpretation of equilibrium charge distributions. J. Math. Kyoto Univ. 4 (1964/1965) 617--625. MR 32 #3130
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X