I'm currently studying for my measure theory final, and I am struggling with a question:
Give an example of a Borel-measurable function X:(0,1)→R that satisfies:
For every a∈(0,1), the function X is Lebesgue-integrable on [a,1],
The limit lim exists and is finite, with \lambda the standard Lebesgue measure,
The function X is not Lebesgue-integrable on (0,1].
I hope someone could help me out,
thanks.
No comments:
Post a Comment