Year: 2026
Type: preprint
Abstract: We show that the formation of the product measure is the only natural way to assign to each tuple of probability measures on measurable spaces a probability measure on the product space. Here, naturality is meant in the sense of category theory and amounts to the condition that the assignment commutes with pushforward along measurable maps. In the standard Borel setting, we also prove an analogous result for relative products over a fixed base probability space. As a corollary, we conclude that the formation of relative products is a lax symmetric monoidal functor.
Source: arXiv (Cornell University)
Authors: Bloch, Victor, Fritz, Tobias
Institution: Universität Innsbruck
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213274248