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Approximate symmetric derivative and monotonicity. (English) Zbl 0586.26004
It is proved that, if f is a measurable function on the real line with the lower approximate symmetric derivative nonnegative, then it is essentially nondecreasing on some interval.

MSC:
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
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