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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

5 votes
Accepted

Chain-rule and change of variables in BV/Sobolev

Your formula can be wrong even if $f$ and $g$ are both Lipschitz. For criteria when such a result holds (and related results) see e.g. Leoni, Giovanni, Morini, Massimiliano: Necessary and sufficient c …
Kusma's user avatar
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1 vote

Can the Riemann integral be defined through a closure/completion process?

Does $$\|f\|:=\inf \left\{ \int_0^1 g(x) dx : |f|\le g \text{ everywhere}, g \text{ a step function} \right\} $$ work? Then $\|\cdot\|$ is a norm on step functions, Cauchy sequences for $\|\cdot\|$ ar …
Kusma's user avatar
  • 336