 Schröder–Bernstein theorem for measurable spaces

The Schröder–Bernstein theorem is a fundamental result in set theory that provides a criterion for the existence of a bijection (one-to-one and onto correspondence) between two sets, given certain conditions about the existence of injections (one-to-one functions) between those sets. In the context of measurable spaces, the theorem can be reformulated to pertain to the measurability of the functions involved.