Measure Integral & Probability is a gentle introduction that makes measure & integration theory accessible to the average third-year undergraduate student The ideas are developed at an easy pace in a form that is suitable for self-study with an emphasis on clear explanations & concrete examples rather than abstract theory For this second edition the text has been thoroughly revised & expanded New features include a substantial new chapter featuring a constructive proof of the Radon-Nikodym theorem an analysis of the structure of Lebesgue-Stieltjes measures the Hahn-Jordan decomposition & a brief introduction to martingales key aspects of financial modelling including the Black-Scholes formula discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework In addition further exercises & examples are provided to encourage the reader to become directly involved with the material