An Analytic Construction of Random Variables in Lebesgue Spaces
Probability
2025-11-03 v1 Functional Analysis
Abstract
This work develops, from a functional analytic perspective, the construction of random variables in Lebesgue spaces L^p. It extends classical notions of measurability, integrability, and expectation to L^p valued functions, using Pettis's theorem and the Riesz representation theorem to define the Bochner integral as a natural generalization of classical expectation.
Keywords
Cite
@article{arxiv.2510.27154,
title = {An Analytic Construction of Random Variables in Lebesgue Spaces},
author = {Hugo Guadalupe Reyna-Castañeda and María de los Ángeles Sandoval-Romero},
journal= {arXiv preprint arXiv:2510.27154},
year = {2025}
}
Comments
16 pages, 7 figures