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Equality of integrals

  1. Jul 6, 2005 #1
    i don't know where to start on this problem. could someone help me please? thanks.

    let [tex] f: A -> R [/tex] be an integrable function, where A is a rectangle. If g = f at all but a finite number of points, show that g is integrable and [tex] \int_{A}f = \int_{A}g. [/tex]
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  3. Jul 6, 2005 #2


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    What about g - f?
  4. Jul 6, 2005 #3


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    Do you mean the Reimann integral? For each value that they are not equal consider a small interval (small enough that only one point of inequality is included). Then |Sup(f)-Sup(g)|=|f(x*)-g(x*)|>0. Then consider the effect of all the points of inequallity on the upper integrals, then likewise for the lower integrals.
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