currently taking Measure and Integration course, which seems to have a different definition of f'.
traditionally,
f'(x)=\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}
but in folland's book, it seems to be defined as
f'(x)=\lim_{r\to 0} \frac{f(x+r)-f(x-r)}{m(B(x,r))}
i was just wondering if these 2 definitions are really the same thing. thanks in advance