Triangular transformations of measures

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Martingale Benamou–Brenier: A probabilistic perspective (2017, background): “Such a map is an example of an “increasing triangular transformation,” as in [16].”
Normalizing Flows: An Introduction and Review of Current Methods (2020, background): “This has been proven formally [9], [68], [99].”
Bernstein flows for flexible posteriors in variational Bayes (2022, unknown): “It is known that bijective triangular maps with sufficient flexibility can map a simple p-dimensional distribution into arbitrary complex pdimensional target distributions [28].”
Normalizing Flows for Probabilistic Modeling and Inference (2019, methodology): “The argument is based on a similar proof of the existence of non-linear ICA by Hyvärinen and Pajunen (1999); a more formal treatment is provided by e.g. Bogachev et al. (2005).”