Consider a sequence of piecewise constant (positive) function in the space $D$ with Skorohod topology such that each of the functions is zero at the origin and any two discontinuities are at least $\delta$ distance apart. I want to know what will be the nature of the limit function if the sequence converge according to Skorohod metric. Is it true that it will also be zero at origin and any two discontinuities are at least $\delta$ distance apart ?
2026-02-23 07:19:22.1771831162
A basic question on convergence in Skorohod metric
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