Article,
Total variation convergence preserves conditional independence
Affiliations
- [1] University of Copenhagen [NORA names: KU University of Copenhagen; University; Denmark; Europe, EU; Nordic; OECD]
Abstract
This note establishes that if a sequence P,n=1,… of probability measures converges in total variation to the limiting probability measure P, and σ-algebras A and B are conditionally independent given H with respect to P for all n, then they are also conditionally independent with respect to the limiting measure P. As a corollary, this also extends to pointwise convergence of densities to a density.
Keywords
Markov properties,
Scheffé’s theorem