These notes were developed in connection with graduate courses in real analysis taught at the University of Central Florida. Several of the notes were prepared in collaboration with graduate students and are made available for educational and scholarly use.
If you use these materials, please acknowledge the source. Comments, corrections, and suggestions are always welcome.
The Daniell Integral
An introduction to the Daniell approach to integration and its relationship to measure-theoretic integration.
Integrals with Values in Banach Spaces and Locally Convex Spaces
A study of vector-valued integration, including integration in Banach spaces and more general locally convex spaces.
Measures
Lecture notes covering measurable sets, measurable functions, measures, and integration.
Positive Measures and Vector Measures
An introduction to positive and vector measures, including fundamental properties and applications in analysis.