Measure Integral Derivative : A Course on Lebesgues Theory This classroom tested text is intended for a one semester course in Lebesgue’s theory. With over 180 exercises the text takes an elementary approach making it easily accessible to both upper undergraduate and lower graduate level students. The three main topics presented are measure integration and differentiation and the only prerequisite is a course in elementary real analysis. In order to keep the book self contained an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results such as the differentiability property of functions of bounded variations are dissected into small steps in order to be accessible to students. With the exception of a few simple statements all results are proven in the text. The presentation is elementary where σ algebras are not used in the text on measure theory and Dini’s derivatives are not used in the chapter on differentiation. However all the main results of Lebesgue’s theory are found in the book. 1 Preliminaries 2 Lebesgue Measure 3 Lebesgue Integration 4 Differentiation and Integration A Measure and Integral over Unbounded Sets Index.