Measure Theory and Lebesgue Integration

This book describes the construction of a general measure theory, emphasizing the significant advantages of the Lebesgue measure. It explains in detail both Jordan's and Lebesgue's constructions. In addition, the book also discusses the similarities and important differences between the two measures. Based on the general set measure theory, this book builds the Lebesgue integral theoretically. The construction is carried out in three consecutive steps. The book also discusses the issue of integrating functions with a parameter and the method of solving integrals using differentiation with the respect to the parameter.