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From: jfh@browngr.UUCP (John "Spike" Hughes)
Newsgroups: net.math
Subject: Re: f(x) = (if x = p/q then 1/q else 0) integrable ??
Message-ID: <1838@browngr.UUCP>
Date: Fri, 8-Feb-85 10:34:24 EST
Article-I.D.: browngr.1838
Posted: Fri Feb  8 10:34:24 1985
Date-Received: Mon, 18-Feb-85 04:46:39 EST
References: ucbvax.4467, <350@decwrl.UUCP>
Lines: 9


In this case, the function *is* integrable, but if one sets
   f(x) = (if x=p/q then x else 0)

you get a function that is Lebesgue integrable but not Riemann integrable.
It may well be true that there is a more restictive notion of integral than
Riemann integration under which functions like f(x) = (if x = p/q then 1/q\else 0)
are *not* integrable.
  -jfh