Presents the Lebesgue integral at an accessible undergraduate level with surprisingly minimal prerequisites. The key is the text’s use of a method labelled the Daniell-Riesz approach. The treatment is self-contained, and so the associated course, often offered as Real Analysis II, no longer needs Real Analysis I as a prerequisite.
This text presents the Lebesgue integral at an accessible undergraduate level with surprisingly minimal prerequisites. Anyone who has mastered single- variable calculus concepts of limits, derivatives, and series can learn the material. The key to this success is the text.s use of a method labeled the .Daniell-Riesz approach. The treatment is self-contained, and so the associated course, often offered as Real Analysis II, no longer needs Real Analysis I as a prerequisite. Additional curricular options then exist. Academic institutions can now offer a course on the integral (and function spaces) along with Complex Analysis and Real Analysis I, where completion of any one course enhances the other two. Students can enroll immediately after Calculus II, after a first course in mathematical proofs, or as a required course in function theory. Along with Vector Calculus and Probability Theory, this set of courses now provides a comprehensive undergraduate investigation into functions.