Thanx for the answer (though, because my english has gotten a bit rusty, and with no practice in 'math'english, the answer isnt all that clear), but could you explain the diference between these two functions (from the aspect of Riemann integrability)
f(x) is the Dirichlet function metioned before (0 when x irational, 1/q when x=p/q, Riemann intabrible, integral = 0 )
g(x) = 1 if x is rational
0 if x is irational
wouldn't your ansewr apply to this function too? On an arbitrary interval [a,b] -> Lebesgue mesure is zero -> etc. But if you consider the definition of the Riemann integral, (I don't know what's it called in english, ???the higher/upper aproximation sum ( S(f,T) )??? and the ???lower aprox.sum ( s(f,T) )???? ). )
for g to be integrable inf{ S(g,T) } = sup{ s(g,T } should be true, but s(g,t)=0 (const) and S(g,t)=1 (const) so g() not Riemann integrable.)
hope I wasnt too confusing, my english with math termiology is not so good... I hope you can figure out what I wanted to say
Thanx
emil
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