Let $f$ be a function defined on an interval $[a,b]$ with bounded variations. The application $|.|: f \mapsto |f|=v(f) + |f(a+)|$, where $v(f)$ is the total variation of $f$, is a norm.
Why do we need to add the term $|f(a+)|$ ?
2026-03-28 20:03:31.1774728211
Norm for bounded variations function
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$v(f)=0$ does in general not imply that $f(x)=0$ for all $x \in [a,b]$ !