nLab
Meas

Meas is the category of measurable spaces. The objects are measurable spaces (sets equipped with σ\sigma-algebras), and the morphisms are measurable functions.

Discussion

Urs: Er, I meant to say here: Meas is the category of measure spaces and measure-preserving maps.

But now I recall that John uses Meas for a 2-categorical version of that.

Which terminology should we use? What’s the standard term for the category of measure spaces?

Toby: You can distinguish them as MeasSp\MeasSp and MeasCat\MeasCat. But by default, I would expect Meas\Meas to mean MeasSp\MeasSp. (Unless there was some sense that MeasSp\Meas\Sp can be built out of Sp\Sp and some operator Meas\Meas, kind of like how GrayCat\Gray\Cat is GrayCat\Gray‑\Cat for suitable Gray. But life is probably not that beautiful.)

Tom: The category of measured spaces is notoriously difficult to work with from the structural point of view. I suggest that Meas refer to the more basic category whose objects are measurable spaces and morphisms are measurable functions.

category: category

Revised on March 27, 2013 17:59:29 by Anonymous Coward (82.45.115.180)