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arXiv · 2003.10787

On the completion of Skorokhod space

Mikhail Lifshits·Vladislav Vysotsky
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Abstract

We consider the classical Skorokhod space $D[0,1]$ and the space of continuous functions $C[0,1]$ equipped with the standard Skorokhod distance $\rho$. It is well known that neither $(D[0,1],\rho)$ nor $(C[0,1],\rho)$ is complete. We provide an explicit description of the corresponding completions. The elements of these completions can be regarded as usual functions on $[0,1]$ except for a countable number of instants where their values vary "instantly".

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Mikhail Lifshits, Vladislav Vysotsky. 2020-03-24. On the completion of Skorokhod space. https://arxiv.org/abs/2003.10787

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