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We introduce a more restrictive version of the strict $CD(K,\infty)$-condition, the so-called very strict $CD(K,\infty)$ -condition, and show theexistence of optimal maps in very strict $CD(K,\infty)$ -spaces despite thepossible lack of uniqueness of optimal plans.

Existence of optimal transport maps in very strict $CD(K,\infty)$ -spaces