The group of measure preserving transformations of the unit interval is an absolute retract

Nguyen To Nhu
1990 Proceedings of the American Mathematical Society  
The group of measure preserving transformations of the unit interval equipped with the weak topology is an absolute retract, hence is homeomorphic to a separable Hubert space.
doi:10.1090/s0002-9939-1990-1009997-6 fatcat:gsnuslqa65ekdngsqygria3h6i