Hi

I have been working with the topic Lebesgue integration for some time, but I have some questions.

Lets say the the function where and

I will like to show for which values of that this function f(x) is integratable in 0 and and finally can be integrated over the

I have a feeling that first I first need to show that f(x) is a messurable function which is also know as a Borel function. I know that my function is mesurable if its continous. Since the preimage of f(x) is open, then this is obviously continous, and therefore a Borel function.

According to the definion I know of Local Lebesgue integratable functions, then if

is called Lebesgue Integratable if for every compact subset subset

Thus for every compact subset

Could someone here please give me a hint how I by applying this definition Lebesgue integratable function on my function can find the desired values of ??

best Regards

Billy