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.
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.