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In the answer to the following comment, it is shown why $\rho(x,x') = 0$ implies $x = x'$: http://math.stackexchange.com/questions/163678/a-proof-that-skorohod-metric-is-a-metric

In the answer to the following comment, it is shown why $\rho(x,x') = 0$ implies $x = x'$: https://math.stackexchange.com/questions/163678/a-proof-that-skorohod-metric-is-a-metric

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In the answer to the following comment, it is shown why $\rho(x,x') = 0$ implies $x = x'$: http://math.stackexchange.com/questions/163678/a-proof-that-skorohod-metric-is-a-metric