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Proceedings of the American Mathematical Society

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A counterexample related to a criterion for a function to be continuous


Author: J. Michael Steele
Journal: Proc. Amer. Math. Soc. 79 (1980), 107-109
MSC: Primary 60G17; Secondary 26A15
MathSciNet review: 560594
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Abstract | References | Similar Articles | Additional Information

Abstract: A construction is given of a right-continuous function which satisfies an arithmetic continuity condition, but which is not continuous. The problem is motivated by a familiar criterion for the continuity of sample paths of a stochastic process.


References [Enhancements On Off] (What's this?)

  • [1] A. Ya. Khintchin, Continued fractions, Univ. of Chicago Press, Chicago, Ill., 1964.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0560594-X
Keywords: Continuous path, continuity criterion, quadratic irrational
Article copyright: © Copyright 1980 American Mathematical Society