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math.FA2025
Inductive Volume Measure: A Geometric Alternative to Hausdorff Measure
Luis A. Cedeño-Pérez
We employ methods of geometry and generalized convergence to construct a geometric measure that serves as an alternative to the integer-dimension Hausdorff measure. This constructi…
math.FA2024
Smooth Functional Calculus and Spectral Theorem in Banach Spaces
Luis A. Cedeño-Pérez, Hernando Quevedo
The notion of projection families generalizes the classical notions of vector- and operator-valued measures. We show that projection families are general enough to extend the Spect…
math.FA2024
A General Theory of Operator-Valued Measures
Luis A. Cedeño-Pérez, Hernando Quevedo
We construct a new kind of measures, called projection families, which generalize the classical notion of vector and operator-valued measures. The maximal class of reasonable funct…