Pacific Journal of Mathematics

Positive analytic capacity but zero Buffon needle probability.

Peter W. Jones and Takafumi Murai

Article information

Source
Pacific J. Math., Volume 133, Number 1 (1988), 99-114.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102689569

Mathematical Reviews number (MathSciNet)
MR936358

Zentralblatt MATH identifier
0653.30016

Subjects
Primary: 30C85: Capacity and harmonic measure in the complex plane [See also 31A15]

Citation

Jones, Peter W.; Murai, Takafumi. Positive analytic capacity but zero Buffon needle probability. Pacific J. Math. 133 (1988), no. 1, 99--114. https://projecteuclid.org/euclid.pjm/1102689569


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References

  • [1] J. Garnett,Analytic Capacity and Measure, Lecture Notes in Mathematics, Vol. 297, Springer-Verlag, Berlin/New York, 1972.
  • [2] L. D. Ivanov, On sets of analytic capacity zero, in Linear and Complex Analysis Problem Book (Edited by V. P. Havin, S. V. Hruscev and N. K. Nikol'skii), Lecture Notes in Mathematics, Vol. 1043, Springer-Verlag, Berlin/New York, 1984, 498-501.
  • [3] D. E. Marshall, Removable sets for bounded analytic functions, in Linear and Complex Analysis Problem Book (Edited by V. P. Havin, S. V. Hruscev and N. K. Nikol'skii), Lecture Notes in Mathematics, Vol. 1043, Springer-Verlag, Berlin/New York, 1984, 485-490.
  • [4] P. Manila, Smooth maps, null-sets for integral geometric measure and analytic capacity,Annales of Math., 123 (1986), 303-309.
  • [5] T. Murai, Comparison between analytic capacity and the Buffon needle proba- bility, Trans. Amer. Math. Soc. 304 (1987), to appear.
  • [6] L. A. Santal, Introduction to Integral Geometry, Hermann, 1953.
  • [7] A. G. Vitushkin, Analytic capacityof sets and problems in approximation theory, Russian Math. Surveys, 22 (1967), 139-200.