A Counterexample Related to a Criterion for a Function to be Continuous
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Continuous path
continuity criterion
quadratic irrational
Mathematics
continuity criterion
quadratic irrational
Mathematics
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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.
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1980-05-01
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Proceedings of the American Mathematical Society