Continuous Functions that Cut the Real Axis Very Often
classification
🧮 math.CA
keywords
axiscontinuousfunctionsrealadmitsboundedconsiderconstruct
read the original abstract
We consider continuous functions f : [0,1] \to R that cut the real axis at every point of a measurable set of positive measure and we construct examples where f fails to have bounded variation, and at the opposite end, where f admits derivatives of all orders.
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