Thursday, 28 February 2013

Nowhere continuous real valued function which has an antiderivative

My question:



Is there a function f:RR that nowhere continuous on its domain, but has an antiderivative?



If there is no such a function, is it true to conclude that: to have an antiderivative, f is necessary to be continuous at least at one point on its domain?



Any comments/ inputs are highly appreciated. Thanks in advance.

No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...