This text is geared towards students who have no prior exposure to measure theory or advanced probability, and who require this material for their work in statistics, applied probability, operations research, mathematical finance, and engineering.

A one semester path is laid out in an efficient and disciplined way to cover the core material. The first three chapters provide a functioning knowledge of measure theory, Chapter 4 discusses independence, with expectation and integration covered in Chapter 5. This is followed by topics on different modes of convergence, laws of large numbers with applications to statistics (quantile and distribution function estimation) and applied probability. The remaining chapters offer a careful treatment of convergence in distribution and the central limit theorem. Finally, the text treats conditional expectation and martingales, closing on the fundamental theorem of mathematical finance.