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.
Kernel mean embedding of distributions: A review and beyond.Foundations and Trends in Machine Learning, 10(1-2):1–141, 2017
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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.