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Explore the innovative concept of measure-theoretic Reeb graphs in this 56-minute lecture from the Applied Algebraic Topology Network. Delve into a novel construction of Reeb graphs that incorporates measures, enhancing their robustness in representing topological features of scalar fields. Learn about the stability of Reeb graphs with local smoothing and their application to metric measure spaces. Discover how these advanced techniques utilize distance to measure and kernel distance to measure, providing a more comprehensive understanding of scalar functions on topological spaces.
