TITLE: Category for measure spaces?
QUESTION [7 upvotes]: I know some things about measures/probabilities and I know some things about categories. Shortly I realized that uptil now I have never encountered something as a category of measure spaces. It seems quite likely to me that something like that can be constructed. I am an amateur however and my scope is small. I have two questions:

1 Is there indeed material of this sort and can you tell me about it? The whereabouts for instance.
2 Is there a reason for the fact that uptil now I did not find anything of the sort? Is it indeed rare for some reason?

REPLY [5 votes]: This has been asked before:

Is there an introduction to probability theory from a structuralist/categorical perspective?

And for the notion of product:

Can one view the Independent Product in Probability categorially?
Is there a category structure one can place on measure spaces so that category-theoretic products exist?