Category of measurable spaces

In mathematics, the category of measurable spaces, often denoted Meas, is the category whose objects are measurable spaces and whose morphisms are measurable maps.^[1][2][3][4] This is a category because the composition of two measurable maps is again measurable, and the identity function is measurable.

N.B. Some authors reserve the name Meas for categories whose objects are measure spaces, and denote the category of measurable spaces as Mble, or other notations. Some authors also restrict the category only to particular well-behaved measurable spaces, such as standard Borel spaces.