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Results tagged with real-analysis
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user 90407
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
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 …
- 336
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 …
- 336