Coproduct Measure

Michikazu Hirata 📧

June 4, 2024

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

This entry formalizes the coproduct measure. Let I be a set and {Mi}iI measurable spaces. The σ-algebra on iIMi={(i,x)iIxMi} is defined as the least one making (λx.(i,x)) measurable for all iI. Let μi be measures on Mi for all iI and A a measurable set of iIMi. The coproduct measure iIμi is defined as follows: (iIμi)(A)=iIμi(Ai),where Ai={x(i,x)A}. We also prove the relationship with coproduct quasi-Borel spaces: the functor R:MeasQBS preserves countable coproducts.

License

BSD License

Topics

Session Coproduct_Measure