| Author: | Truman Arthur Botts, Edward James McShane | ISBN: | 9780486165677 |
| Publisher: | Dover Publications | Publication: | November 7, 2013 |
| Imprint: | Dover Publications | Language: | English |
| Author: | Truman Arthur Botts, Edward James McShane |
| ISBN: | 9780486165677 |
| Publisher: | Dover Publications |
| Publication: | November 7, 2013 |
| Imprint: | Dover Publications |
| Language: | English |
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. Helpful exercises appear throughout the text. 1959 edition.
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. Helpful exercises appear throughout the text. 1959 edition.
