Let be a measurable subset of with and let be a real-valued measurable function on . Prove that for any , there exists a bounded measurable function on such that .

Again, how do I go about doing it? Thanks in advance.

Printable View

- September 25th 2011, 11:08 AMMarkeurMeasurable Functions (2)
Let be a measurable subset of with and let be a real-valued measurable function on . Prove that for any , there exists a bounded measurable function on such that .

Again, how do I go about doing it? Thanks in advance. - September 25th 2011, 02:35 PMTinybossRe: Measurable Functions (2)
Okay, so what's the main issue here? If you just let , then the measure of the set where they differ is certainly less than . But of course, then may not be bounded as required. So try defining , and looking at what happens to as goes to infinity.

- September 26th 2011, 07:39 AMMarkeurRe: Measurable Functions (2)
Okay managed to solved it. Though I used g(x) = f(x) if x lies in A, g(x) = 0 otherwise.

Thanks anyway.