Is right differentiable function almost everywhere continuous? If not, is it measurable?
Is right differentiable function almost everywhere continuous?
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real-analysis
measure-theory
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0For clarity, could you define "right differentiable" and "almost everywhere continuous"? – 2011-12-27
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0I think I retagged it properly. Measure theory was added – 2011-12-27
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0function f(x) is defined on [a,b). It is right differentiable which means for any x in [a,b), lim y->x (f(y)-f(x))/(y-x) exists. – 2011-12-27
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0And almost everywhere continuous means the discontinuous points of f(x) constitute a measure-zero set. – 2011-12-27