Skorohod’s spaces.(English)Zbl 0901.60009

The author defines a pseudometric with possible infinite values on the space of all real-valued functions defined on a rather general set $$T$$. The construction follows the idea of Skorokhod metric on the space of right-continuous functions on $$[0,1]$$ which have left-limits at every point. It uses a normed group of automorphisms acting on $$T$$ which can be used to transform the parameters on functions in order to bring them “close to each other” in the uniform metric penalised by the norm of the automorphism. The author shows that the introduced pseudometric space is complete and the factor space of equivalent functions is a Hausdorff space. Relatively compact sets of functions and Radon probability measures are characterised.

MSC:

 60B10 Convergence of probability measures 54C35 Function spaces in general topology
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