Introduction
Measure theory is a branch of mathematics that extends the concepts of length, area, volume, and probability. It provides a rigorous foundation for these ideas, making them applicable to a wider range of sets and functions.
Contents
Measure-theoretical Real Analysis
The Exterior Measure
Borel Sets and Real Valued Measurable Functions
Lebesgue Measurability
Lebesgue Measurable Functions
Littlewood’s Three Principles
Lebesgue Integration
Absolute Continuous Functions
The Space of Integrable Functions
Function Spaces
Lebesgue Differentiation Theorem
Abstract Measures
Measurable Spaces and Functions
Convergence Theorems
Integration on Measure Spaces
Absolute Continuity
Projection Valued Measures
More …
References
Terence Tao, An Introduction to Measure Theory
Sheldon Axler, Measure, Integration & Real Analysis
Elias M. Stein and Rami Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces