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Multivariable calculus

  1. Mar 31, 2009 #1
    let g:[a,b] -> R be a function that is continuous almost everywhere. assume that g(x) > 0 on [a,b]. Show that the set
    S = { (x,y): 0 <= y <= g(x) , a <= x <= b} is rectifiable.

    One way to attack it, is to show that S is bounded and boundary of S has measure zero. the problem im having is how to show that S is bounded, since g is continuous a.e. I don't now whether or not g is bounded on [a,b].

    any comments at all are strongly appreciated, thanks.
    Last edited: Apr 1, 2009
  2. jcsd
  3. Apr 1, 2009 #2
    forgot to mention the definition of rectifiable here: a (bounded) set S is rectifiable if

    [tex]\int_{S} 1[/tex] exists. (so it has volume.)

    Last edited: Apr 2, 2009
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