Coarse-Graining of Observables
Round 1
Reviewer 1 Report
The definition of coarse graining of probability measures via stochastic kernels seems to be well substantiated by examples. Also, the extension of stochastic kernels to stochastic matrices for finite dimensional situations seems to be interesting. So I would recommend this for publication.
Author Response
Thank you for your comments. I’m glad you liked the paper.
Reviewer 2 Report
The paper is conceived as a rather formal pure mathematics paper. Many of the results do not seem to me to be surprising at all, and I think that much shorter heuristic proofs could easily have been given. That's not the style of this author. It does mean that his readership will be quite limited. Towards the end of the paper, the author arrives at speculations concerning interesting open problems. The paper therefore does formulate an interesting open mathematical problem for the future. Altogether, I think the paper is a useful addition to the scientific record.
Author Response
Thank you for your comments. I found them useful.