Remarks on a Multivariate Transformation. M. Rosenblatt in Ann. Math. Stat. 23:470 (1952).  What the paper says!?

The paper provides the way to map a multivariate distribution to the uniform one (in the hypercube with the corresponding number of dimensions):

This is needed for, but apparently does not immediately provide, a technique of multivariate inverse random sampling, which is a problem of interest to us. To quote that technique, which appears to be a more or less straightforward application of this result from Rosenblatt, it is probably better to cite, e.g., 🕮Handbooks in Operations Research and Management Science, chapter "4. Nonuniform Random Variate Generation", p. 83. L. Devroye. North Holland, 2006. [DOI: 10.1016/s0927-0507(06)13004-2] or Mark E. Johnson's "Multivariate Statistical Simulation" book (subtitled "A Guide to Selecting and Generating Continuous Multivariate Distributions")

A comment on this paper from an obituary:[1]