An Analytic Construction of Random Variables in Lebesgue Spaces
Abstract
This work develops, from a functional analytic perspective, the construction of random variables in Lebesgue spaces Lp. It extends classical notions of measurability, integrability, and expectation to Lp valued functions, using Pettis's theorem and the Riesz representation theorem to define the Bochner integral as a natural generalization of classical expectation.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.