Lebesgue Measure and Integration Theory: Foundations and Solved Exercises offers a thorough, engaging introduction to Lebesgue measure and the theory of integration for students of mathematics and physics. This book provides the complete theoretical underpinnings of this theory, with the corresponding proofs, adapted to the level of advanced undergraduate and graduate students in these disciplines. Beginning with a fundamental discussion of measure spaces, the book moves onto measurable and non-measurable sets, approximation of measurable sets, measurable functions, the Lebesgue integral, the relationship between differentiation and integration on R, and product measures, among other topics. Examples and solved exercises are included across chapters to reinforce understanding and application. - Provides a thorough, engaging discussion of Lebesgue measure and integration theory for students of mathematics and physics - Highlights different aspects of measure theory, and places special emphasis on the existence of non-measurable sets and notable examples - Considers measurable and non-measurable sets, measurable functions, generation of measure spaces, the Lebesgue-Stieltjes measure space in R and Rn, and product measures, among other topics - Includes proofs, examples, and solved exercises across all chapters