Abstract
Let f:X→X be a contracting homeomorphism of a metric space with positive diameter. We prove that the induced map f⁎ in the space of probability measures equipped with the Prokhorov metric does not have the shadowing property. However, if X is Polish, then the restriction of f⁎ to the Wasserstein space has the generalized shadowing property as per Boyarsky and Gora [4], concerning the Kantorovich-Rubinstein and Prokhorov metrics.
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