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A 22-minute lecture by Ondřej Kalenda exploring the generalizations of Choquet theory to vector-valued function spaces, presented at the Workshop on "Structures in Banach Spaces" at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Discover recent research results developed jointly with Jiří Spurný that address the challenge of creating a satisfactory theory of uniqueness of representing measures in vector-valued settings. Learn about two natural directions for generalization—weak simpliciality and vector simpliciality—and understand how these concepts compare, with vector simpliciality being strictly stronger for function spaces containing constants. The presentation highlights both similarities and differences between these vector-valued approaches and the traditional scalar theory, providing insights into this specialized area of mathematical analysis.
