Riemann integral problem

  • Thread starter losin
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  • #1
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suppose f and g are bounded functions on [a,b] such that f+g is in R[a,b]

Then, does it follow that f and g are also in R[a,b]? i wanto to prove whether it is or not
 

Answers and Replies

  • #2
mathman
Science Advisor
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Not so. Let f be a function which is NOT Riemann integrable and let g=1-f.

For example f(x)=1, when x is irrational and f(x)= 0, when x is rational.
 

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