Kernel covariance embeddings of non-atomic Borel probability measures on locally compact Polish spaces induce singular centered Gaussians in the RKHS, making equality testing equivalent to singularity testing via the Feldman-Hajek dichotomy.
Sur une classe d’´ equations fonctionnelles.Acta Mathematica, 27(1):365–390
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Kernel Embeddings and the Separation of Measure Phenomenon
Kernel covariance embeddings of non-atomic Borel probability measures on locally compact Polish spaces induce singular centered Gaussians in the RKHS, making equality testing equivalent to singularity testing via the Feldman-Hajek dichotomy.