Abstract
In this chapter, we consider random elements taking values in metric spaces and their distributions. The definition of a random element taking values in \({{\Bbb X}}\) involves the predefined \(\sigma\)-algebra \({{\rm X}}\) of subsets of \({{\Bbb X}}\). The following statement shows that in a separable metric space, in fact, the unique natural choice for the \(\sigma\)-algebra \({{\rm X}}\) is the Borel \(\sigma\)-algebra \({{\rm B}}({{\Bbb X}})\).
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Gusak, D., Kukush, A., Kulik, A., Mishura, Y., Pilipenko, A. (2010). Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems. In: Theory of Stochastic Processes. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-87862-1_16
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DOI: https://doi.org/10.1007/978-0-387-87862-1_16
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Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-87861-4
Online ISBN: 978-0-387-87862-1
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