An Analytic Construction of Random Variables in Lebesgue Spaces
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866908622495154176 |
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| author | Reyna-Castañeda, Hugo Guadalupe Sandoval-Romero, María de los Ángeles |
| author_facet | Reyna-Castañeda, Hugo Guadalupe Sandoval-Romero, María de los Ángeles |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Analytic Construction of Random Variables in Lebesgue Spaces Reyna-Castañeda, Hugo Guadalupe Sandoval-Romero, María de los Ángeles Probability Functional Analysis 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. |
| title | An Analytic Construction of Random Variables in Lebesgue Spaces |
| topic | Probability Functional Analysis |
| url | https://arxiv.org/abs/2510.27154 |