Название: Real Analysis
Серия: University Series in Undergraduate Mathematics
Автор: Edward James and Truman Arthur Botts McShane
Издательство: D. Van Nodstrand
Год: 1959
Формат: djvu
Страниц: 280
Размер: 17,6 Мб
Язык: английский
This text offers upper-level undergraduates and graduate students a survey of practical elements of real function theory, general topology, and functional analysis. Beginning with a brief discussion of proof and definition by mathematical induction, it freely uses these notions and techniques. The maximality principle is introduced early but used sparingly; an appendix provides a more thorough treatment. The notion of convergence is stated in basic form and presented initially in a general setting. The Lebesgue-Stieltjes integral is introduced in terms of the ideas of Daniell, measure-theoretic considerations playing only a secondary part. The final chapter, on function spaces and harmonic analysis, is deliberately accelerated.