At the request of another user, I am taking an older question and specifically addressing one problem.
I am self-learning about Lebesgue integration, and am just starting to try and apply some examples of the existence of the integral.
For the function below, does the Lebesgue integral exist on $(0,\infty)$, and if it does, is it finite?
Since this is self-learning from scratch, I would be grateful if someone could help me break this down bit by bit:
1) What does it mean for the integral to "exist"? Is this just saying that $\int f(x)$ is finite?
2) How do you calculate the integral explicitly?
Any help is always appreciated. Thanks!