A Counterexample Related to a Criterion for a Function to be Continuous

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Continuous path
continuity criterion
quadratic irrational
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Steele, John M
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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.

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1980-05-01
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Proceedings of the American Mathematical Society
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