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Multivariable calculus

  • Thread starter johnson12
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  • #1
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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.
 
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Answers and Replies

  • #2
18
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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.)


update: PROBLEM HAS BEEN SOLVED.
 
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