3 papers
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…
An Analytic Construction of Random Variables in Lebesgue Spaces
Hugo Guadalupe Reyna-Castañeda, María de los Ángeles Sandoval-Romero
This work develops, from a functional analytic perspective, the construction of random variables in Lebesgue spaces L^p. It extends classical notions of measurability, integrabilit…
Variational proof of conditional expectations
Hugo Guadalupe Reyna Castañeda, María de los Ángeles Sandoval-Romero
In this paper, we show that the conditional expectation of a random variable with finite second moment given a -algebra is the unique critical point of an energy functional in H…