Steele, John M2023-05-232023-05-231980-05-012016-06-20https://repository.upenn.edu/handle/20.500.14332/42200A 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.© Copyright 1980 American Mathematical SocietyContinuous pathcontinuity criterionquadratic irrationalMathematicsArticle