I want to find a example of Borel measurable function which is not continuous.
I think that it is a simple or step function or semicontinuous function.
Please help me for find it.
Thanks.
measure-theoryreal-analysis
I want to find a example of Borel measurable function which is not continuous.
I think that it is a simple or step function or semicontinuous function.
Please help me for find it.
Thanks.
Best Answer
The indicator function on $\mathbb Q$ is borel measurable but is nowhere continuous.