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From: wjafyfe@watmath.UUCP (Andy Fyfe)
Newsgroups: net.math
Subject: Re: f(x) = (if x = p/q then 1/q else 0) integrable ??
Message-ID: <11247@watmath.UUCP>
Date: Fri, 1-Feb-85 13:09:58 EST
Article-I.D.: watmath.11247
Posted: Fri Feb  1 13:09:58 1985
Date-Received: Fri, 1-Feb-85 23:44:14 EST
References: <350@decwrl.UUCP> <ucbvax.4467> <589@oddjob.UChicago.UUCP> <11212@watmath.UUCP>
Reply-To: wjafyfe@watmath.UUCP (Andy Fyfe)
Organization: U of Waterloo, Ontario
Lines: 7
Summary: 

It is Lebesgue's Theorem that completely characterizes all bounded Riemann
integrable functions (over [a,b]).  It states that 
	a bounded function f on [a,b] is Reimann integrable if and
	only if the set of points at which f is discontinuous has
	measure zero.

Just in case there was still any doubt about f(x)......