by quantumformalism.academy This is a preview of our upcoming course, Measure Theory and Functional Analysis (Module I), which will be released on a biweekly basis starting from 30 April.
This module will introduce the foundational concepts of measure theory that are essential for understanding the material in Module II, which will focus on Functional Analysis. As such, we will cover the following:
- Real Analysis Review (including the Riemann Integral)
- Sigma Algebras
- Measures
- Outer Measures
- Borel Measures
- Measurable Functions
- Integration of Positive Functions
- Riemann Integral versus Lebesgue Integral
- Modes of Convergence
- Fubini – Tonelli Theorem