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Absolutely continuous

  1. Apr 27, 2010 #1
    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 [tex] f [/tex] on some inteval [tex] [a,b] [/tex] 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. jcsd
  3. Apr 27, 2010 #2

    mathman

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    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
  4. Apr 28, 2010 #3
    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
     
  5. Apr 28, 2010 #4

    mathman

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