Measure Spaces and Measurable Functions: Book 1

This is the first book in a set of ten written for professionals in quantitative finance. These books fill a gap between informal developments in mathematics found in introductory materials and more advanced materials that summarize without formal developing the important results professionals need to learn and employ.

Book 1 in the Foundations in Quantitative Finance Series covers measure theory, including the Riemann and Lebesgue Integral, measurable functions, Borel measures in R, and Littlewood's three principles, a rarity in books on these topics. It lays the foundation for the subsequent volumes.

The overriding goal of these books is a complete and detailed development of the many mathematical theories and results one finds in popular resources in finance and quantitative finance. Each book is dedicated to a specific area of mathematics or probability theory, with applications to finance that are relevant to the needs of professionals. A range of practitioners, students, and researchers will find these books valuable to their career development.

All ten volumes are completely self-referencing. The reader can enter the collection at any point or topic of interest, and then work backwards to identify and fill in needed details. This approach also works for a course on a given volume, with earlier books used for reference. In addition, these volumes support both course-based and self-study approaches to a variety of sequential studies.

The field of quantitative finance books typically develop materials with an eye to comprehensiveness in the given subject matter, yet not with an eye toward efficiently curating and developing the theories needed for applications in quantitative finance. This book and series of volumes fills this need.