Can you visually understand absolute continuity of a function over an interval?

[cappadonza]

i'm having a difficult time trying to grasp what absolute continuity means, i understand uniform continuity. i can't seem to distinguish between the them.
to me it seems that if f on some inteval [a,b] is uniformly continuous then it would be absolutely continuous ?
is there a visual way of describing/thinking about absolute continuity of a function over some interval

 

[mathman]

Uniform continuity is a global property of a function, that is when using the basic definition, you use the same (δ,ε) for all x in the interval.

Absolute continuity is a local property and is equivalent to having a derivative, which can be integrated to get the original function back.

 

[cappadonza]

thanks for you reply, so absoulte continuity guarantee's the functions has a derivative then ?
if so why, are there any good resources or books, where this is proved/explained in more detailed

 

[mathman]

I don't have any references but any good advanced calculus text will have a full discussion.