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Jul 29, 2022 at 12:10 comment added YCor If $f$ is a concave function mapping 0 to 0 and tending to $\infty$, then $f\circ\ell$ is a length function as soon as $\ell$ is a length function. This makes basically impossible to classify all length functions. (For instance there are sublinear length function growing as fast as any prescribed sublinear function. Also, there are proper length function growing slower than any prescribed function tending to $\infty$.)
Jul 29, 2022 at 7:26 history asked worldreporter CC BY-SA 4.0