# Absolutely continuous

1. Apr 27, 2010

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