An introduction to measure theory with applications to probability

• Grant number: 25/02446-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2025
• End date: April 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Victor dos Santos Ronchim
• Grantee: Lucas Duarte Queiroz
• Host Institution: Faculdade de Ciências Agronômicas (FCA). Universidade Estadual Paulista (UNESP). Campus de Botucatu. Botucatu , SP, Brazil

Abstract

This Scientific Initiation project aim the study of classical results regarding measure theory, that are fundamental for a systematic study of probability theory. Among the results we highlight the Borel-Cantelli theorem as an introduction for the Kolmogorov's zero-one law, the Radon-Nikodym theorem and its consequences for the measure and probability theories: The Riesz Theorem that characterizes the duals of $L_p(\mu)$ spaces and the study of conditional probability.