From Classical to Modern Analysis

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The textbook offers a comprehensive transition from undergraduate analysis to graduate-level measure theory, emphasizing the classical foundations while introducing modern concepts such as metric spaces and Lebesgue integration. It is structured for a two-semester course, focusing on metric spaces and topology to prepare students for the abstraction and rigor required in advanced real analysis. Striking a balance between overly formal and too casual approaches, it serves as an effective resource for students aiming to deepen their understanding of real analysis.