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A metrization of \(D_ E[0,1]\) space. (English) Zbl 0857.54027

Given a metric space \((E,r)\), let \(D_E[0,1]\) denote the space of all \(E\)-valued functions on \([0,1]\) which are right continuous on \([0,1)\) and have left-side limits everywhere on \((0,1]\).
Following the metrization of \(D_E[0,\infty)\) given in [S. N. Ethier and T. G. Kurtz, Markov processes, characterization and convergence (1986; Zbl 0592.60049)] the author introduces a new distance \(\rho\) in \(D_E[0,1]\) and shows that \(\rho\) determines a topology that is weaker than Skorokhod topology. Also, a condition for convergence in the Skorokhod topology is given.

MSC:

54E35 Metric spaces, metrizability
60J99 Markov processes
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)

Citations:

Zbl 0592.60049
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