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math.HO2026
Introduction to Measure and Integration Theory
Hugo Guadalupe Reyna-Castañeda, María de los Ángeles 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…
math-ph2026
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…