Meas

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

*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 $\MeasSp$ and $\MeasCat$. But by default, I would expect $\Meas$ to mean $\MeasSp$. (Unless there was some sense that $\Meas\Sp$ can be built out of $\Sp$ and some operator $\Meas$, kind of like how $\Gray\Cat$ is $\Gray‑\Cat$ 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

Last revised on March 27, 2013 at 17:59:29. See the history of this page for a list of all contributions to it.