Analysis

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This third volume concludes our introduction to analysis, completing the groundwork necessary for further study. Like the previous volumes, it contains more material than can be covered in a single course, making it essential to select a suitable subset for lectures. The remaining content can be addressed in seminars or through independent study. For a quick overview, refer to the table of contents and chapter introductions. This volume is also suitable as background for other courses or for self-study. We hope its insights into advanced analysis will spark curiosity and encourage students to delve deeper into this branch of mathematics. We are grateful for the invaluable assistance from friends, colleagues, staff, and students. Special thanks to Georg Prokert, Pavol Quittner, Olivier Steiger, and Christoph Walker for their critical review of the entire text, helping us eliminate errors and enhance the material. Our appreciation also extends to Carlheinz Kneisel and Bea Wollenmann for their feedback on most of the manuscript. Finally, we owe a debt of gratitude to our “typesetting perfectionist,” whose dedication and expertise with TEX and other software ensured the volume's polished final form, as well as its numerous earlier iterations.