May I plz get some assistance on the following question;

If f and g are integrable on a closed set and f(x)<=h(x)<=g(x) for all x in in that set then h (a function) is integrable on that set.

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- May 12th 2009, 12:31 AMnankorProve or disprove integration proof
May I plz get some assistance on the following question;

If f and g are integrable on a closed set and f(x)<=h(x)<=g(x) for all x in in that set then h (a function) is integrable on that set. - May 12th 2009, 03:09 AMPlato
- May 12th 2009, 05:03 AMputnam120
The statement is false.

Take and on the interval and if and 0 other wise. This shows that the statement is false for the Riemann integral.

For Lebesgue integrable take on a set and is not Lebesgue measurable, and 0 else where. Then is not Lebesgue integrable.