N. L. Carothers Livres

This course in real analysis is directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something of value to specialists and nonspecialists alike. The text covers three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal, down-to-earth style, the author gives motivation and overview of new ideas, while still supplying full details and complete proofs. He provides a great many exercises and suggestions for further study.

Focusing on the classical aspects of Banach space theory, this short course covers three key topics: Schauder bases, Lp spaces, and C(K) spaces. It highlights the postwar revival of the field led by notable mathematicians such as James and Lindenstrauss, showcasing their impactful results. A foundational knowledge of functional analysis and some exposure to abstract measure theory is required, along with a basic understanding of topology, although an appendix is provided for necessary topological concepts.