We consider the general version of Pólya urns recently studied by Bandyopadhyay and Thacker (2016+) and Mailler and Marckert (2017), with the space of colours being any Borel space $S$ and the state of the urn being a finite measure on $S$. We consider urns with random replacements, and show that these can be regarded as urns with deterministic replacements using the colour space $S\times [0,1]$.
"Random replacements in Pólya urns with infinitely many colours." Electron. Commun. Probab. 24 1 - 11, 2019. https://doi.org/10.1214/19-ECP226