Article,
Total variation convergence preserves conditional independence
Contributors
Lauritzen, Steffen Lilholt
0000-0001-7176-6212
[1]
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 , 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 n 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
conditional independence,
conditionally independent with respect,
conditions,
convergence,
convergence of densities,
density,
independence,
independent with respect,
measure P,
measurements,
p-n,
pointwise convergence,
probability,
probability measure P,
probability measures,
respect,
sequence,
variation
