An Analytic Construction of Random Variables in Lebesgue Spaces

Hugo Guadalupe Reyna-Castañeda; María de los Ángeles Sandoval-Romero

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arXiv · 2510.27154

An Analytic Construction of Random Variables in Lebesgue Spaces

Hugo Guadalupe Reyna-Castañeda·María de los Ángeles Sandoval-Romero

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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.

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Hugo Guadalupe Reyna-Castañeda, María de los Ángeles Sandoval-Romero. 2025-10-31. An Analytic Construction of Random Variables in Lebesgue Spaces. https://arxiv.org/abs/2510.27154

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