Invariant metric under deformed Markov embeddings with overlapped supports
Abstract
Due to Cencov's theorem, there exists a unique family of invariant symmetric (0,2)-tensor fields on the space of positive probability measures on a set of n-points indexed by n∈ N under Markov embeddings. We deform Markov embeddings keeping sufficiency, and prove existence and uniqueness of invariant families under the embeddings.
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