6 papers
Introduction to Measure and Integration Theory
Hugo Guadalupe Reyna-Castañeda, MarÃa de los Ãngeles Sandoval-Romero, Luis Antonio Cedeño-Pérez
These notes provide a rigorous and accessible introduction to measure and integration theory, with emphasis on the conceptual transition from the Riemann integral to the Lebesgue i…
Invariant Measures in Hamiltonian Systems: The Analytical Foundations of Statistical Physics
Luis A. Cedeño-Pérez, Alexis E. López-Velázquez
We construct a measure in the hamiltonian function level sets that is invariant under the hamiltonian flow for short times and flow preserving for arbitrarily long times. This allo…
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…
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…
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…
Functional measures associated to operators
Luis A. Cedeño-Pérez, Hernando Quevedo
We show that every operator in has an associated measure on a space of functions and prove that it can be used to find solutions to abstract Cauchy problems, including part…