ABSTRACT
For the applied researcher, mathematical probability is a tool—a means to investigate real-world phenomena. As such, many researchers learn and understand this tool in a language that facilitates direct utilization, often in terms of calculus as taught to undergraduates. Mathematicians, statisticians, and a few other disciplines will have learned mathematical probability in terms of measure theory. Not only does this mathematical perspective give them great power in constructing careful proofs in probability theory, it also provides the conceptualization that facilitates an easy translation between real-world problems and mathematical probability. This introduction presents an overview of the key concepts discussed in this book. The book focuses on the basics of measure theory and probability. It also focuses on the implications of measure theory to applied research—the use of a calculus-level mathematical understanding of probability informed by a measure-theoretic conceptualization. The book also introduces probability, statistics, and statistical inference at a level useful for applied research.
