On the distributional transform, Sklar's theorem, and the empirical copula process

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Admissible ways of merging p-values under arbitrary dependence (2020, background): “3 in Rüschendorf [2013] gives the equality with inf in place of min and with P ranging over the probability measures on [0, 1] with the uniform marginals.”
Multivariate Frequency-Severity Regression Models in Insurance (2016, unknown): “, [48].”
Regression diagnostics meets forecast evaluation: conditional calibration, reliability diagrams, and coefficient of determination (2021, background): “1 of Rüschendorf (2009), which implies CEP calibration.”
Copula Theory: An Introduction (2010, unknown): “A multivariate proof, based on the distributional transform, has been recently presented in [174] (compare also with [144, Lemma 3.”
Partial Distributional Policy Effects (2011, unknown): “See Rüschendorf (2009) for details.”
Statistics and Quantitative Risk Management for Banking and Insurance (2014, background): “An analytic proof of Sklar’s Theorem can be found in Sklar (1996), a probabilistic one in Rüschendorf (2009).”