# Absolutely continuous

1. Apr 27, 2010

### cappadonza

i'm having a difficult time trying to grasp what absolute continuity means, i understand uniform continuity. i cant seem to distinguish between the them.
to me it seems that if $$f$$ on some inteval $$[a,b]$$ is uniformly continous then it would be absolutely continuous ?
is there a visual way of describing/thinking about absolute continuity of a function over some interval

2. Apr 27, 2010

### 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.

Last edited: Apr 27, 2010
3. Apr 28, 2010

### 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

4. Apr 28, 2010

### mathman

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

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