= Skorokhod space
{c}
{title2=$D([0,1],\mathbb R)$}
The Skorokhod space consists of real paths that are <right-continuous> and have a finite left limit at every positive time. Its $J_1$ topology allows small changes of time: $x_n\to x$ when there are increasing homeomorphisms $\lambda_n$ of $[0,1]$ such that $\|\lambda_n-\mathrm{id}\|_\infty\to0$ and $\|x_n\circ\lambda_n-x\|_\infty\to0$, where $\mathrm{id}$ denotes the identity time map. This topology aligns nearby jumps rather than insisting on uniform closeness at identical times. The step-path version of the <Donsker invariance principle> converges here to continuous <Brownian motion>; its polygonal version uses the ordinary <supremum norm> on continuous paths.
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