Equivalence-singularity dichotomies from zero-one laws
Equivalence-singularity dichotomies from zero-one laws
In this note a general result on equivalence and singularity of two measures is presented.As a consequence of this S. Kakutani's dichotomy for product measures and J. Feldman's dichotomy for Gaussian measures are derived via appropriate zero-one laws.In several different contexts, probability measures P, Q which are mutually absolutely continuous …