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Equality of integrals

  • Thread starter jeanf
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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]
 

Hurkyl

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What about g - f?
 

lurflurf

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jeanf said:
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]
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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