All questions with tag [math: absolute-continuity]


Why is the Cantor function not absolutely continuous?

Is there a very easy means to see that the Cantor function is not definitely continual that straight makes use of the definition of definitely continual?
2022-07-15 04:05:53

Sobolev space and equivalence of norms

I'm considering the space $W\{n,p\}[0,1]$ of functions with $n-1$ continuous derivatives $f^{(n-1)}$ is absolutely continuous and $f^{(n)}$ is in $L^p[0,1]$. The usual norm is the sum of the $p$-norms of each derivative from $1$ to $n$ and the $p$ norm of the function. Now just consider the $p$ norm of the function + $p$ norm of the $n^{th}$ de...
2022-07-08 06:06:52

Continuous and bounded variation does not imply absolutely continuous

I recognize that a continual function which is a BV might not be definitely continual. Exists an instance of such a function? I was seeking a BV whose by-product is not Lebesgue integrable yet I could not locate one.
2019-05-12 20:09:25