Here are my questions.
- Are $L^\infty$ functions of bounded variation?
- Is the composition of two BV functions still of bounded variation?
- Is $x\mapsto \frac 1{f(x)}$ of bounded variation when $f$ is of bounded variation?
Cheers.
Here are my questions.
Cheers.
As said above: no, no, no. (1) Consider $\sin(1/x)$. (2) Consider $\sqrt{x}$ composed with $x^2\sin^2(1/x)$. (3) Consider $1/x$.