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math.GN2022
Continuous R-valuations
Jean Goubault-Larrecq, Xiaodong Jia
We introduce continuous -valuations on directed-complete posets (dcpos, for short), as a generalization of continuous valuations in domain theory, by extending values of continu…
math.GN2022
A cone-theoretic barycenter existence theorem
Jean Goubault-Larrecq, Xiaodong Jia
We show that every continuous valuation on a locally convex, locally convex-compact, sober topological cone has a barycenter. This barycenter is unique, and the bary…