I was taking a look at some measure theory, and, finding the concept of finite measure space I thought about the following question:
Is there some sort of a conceptual link (in the form of theories or specific theorems) between finite measure spaces and bounded metric spaces?
Now, I am not completely sure this question makes sense, but I was lead to it by the potential analogy that there can be between the original problem of measure and the idea of distance between points as measured in some way.
Any feedback is most welcome.
Thank you for your time.