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Topic: [ap-calculus] Re: integrable
Replies: 1   Last Post: Feb 10, 2002 7:39 PM

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 Dave Marain Posts: 132 Registered: 12/3/04
[ap-calculus] Re: integrable
Posted: Feb 10, 2002 7:39 PM
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Jeff,
Refresh my memory here.
Consider the function f defined on [0,1] as follows:
f(x) = 0 if x = 1/n, n = 1,2,3,...
f(x) = 1, otherwise.
Thus f has infinitely many 'jump' discontinuities, yet I believe that
f is integrable on [0,1] with value = 1.
This is probably what you were saying, but I think a necessary and
sufficient condition for Riemann-integrability is that the number of
such discontinuities be of measure zero, e.g.., a 'countable' number
of discontinuities. Most respondents suggested that there can only be
a finite number of discontinuities. Am I correct here?
Dave Marain

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Date Subject Author
2/10/02 Jeff Stuart
2/10/02 Dave Marain

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