Measure Theory

Overview

Measure theory is an abstract mathematical theory concerned with measuring the "size" of sets, typically thought of as areas or volumes. Its most basic form is the traditional integration analysis that is taught in standard calculus classes.

Measure Theory Definitions

Measure theory includes a set of additional notions that are not present in the standard calculus.

• Measurable Sets - describes what makes a set measurable.
• Measurable Functions - measurable functions are essentially the functions for which an integral can be computed
• Integral: - the measure theoretic definition of the integral which extends the standard Riemann Integral

Foundations

• Monotone Classes: used in the Monontone Class Theorem

Stochastic Integration

Stochastic Integrals