4
$\begingroup$

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.

  • 0
    Here are your answers: no, no, no.2012-10-11

1 Answers 1

4

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 $1/x$.