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Theory of Functions of a Real Variable – I. P. Natanson
This classic textbook, authored by the renowned Soviet mathematician I. P. Natanson, offers a rigorous yet accessible introduction to the theory of functions of a real variable. It covers measurable sets and functions (both single and multiple variables), the Lebesgue integral and its generalizations, summable functions, the Stieltjes integral, absolutely continuous functions, singular integrals, and functions with unbounded domains of definition.
Aligned with university curricula, the book also includes advanced topics in smaller print, extending beyond standard program requirements. A key strength is its clarity and accessibility, making even the most complex reasoning understandable. The text is supplemented with a large number of exercises, ranging from routine to challenging.
Designed for university students, this textbook remains a valuable resource for those seeking a deep understanding of real analysis.