= Metric path length
{title2=$L(\gamma)=\sup_{\mathcal P}\sum_i d(\gamma(t_i),\gamma(t_{i-1}))$}
For a <continuous path> $\gamma:[a,b]\to X$ in a <metric space>, take the <supremum> over finite partitions $a=t_0<\cdots<t_n=b$ of $\sum_{i=1}^n d(\gamma(t_i),\gamma(t_{i-1}))$. This definition allows $+\infty$ and needs no <derivative>. A <metric geodesic> parametrized on $[a,b]$ has length $b-a$. In a <Riemannian manifold>, it agrees with the usual <arc length> integral for a <smooth> curve.
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