Measure Theory/Introduction to the Course

Introduction to the Course

Content

• Lebesgue measure
• Lebesgue integration
• Differentiation and Lebesgue integration
• $L^{p}$ spaces

Prerequisites

• A strong foundation in real analysis (such as that found in Rudin's Principles of Mathematical Analysis).
• We will use some ideas, briefly, from probability theory, statistics, set theory, and others. However, if you have a strong foundation in real analysis, then it should be easy to learn what you need from these subjects as they come up. We will not use them extensively, so it should not be necessary to study them in advance of taking this course.