Colloquium Publications 1948; 572 pp; softcover Volume: 30 ISBN10: 0821846213 ISBN13: 9780821846216 List Price: US$104 Member Price: US$83.20 Order Code: COLL/30
 Radó's colloquium is a systematic treatment of Lebesgue theory, with an emphasis on the work of Morrey and of Radó and his students, especially in two dimensions. At the time, there were important current problems surrounding Lebesgue's theory for parameterized and unparameterized surfaces, which the book addresses. The exposition begins with reviews of Lebesgue integration and relevant topics in topology, including Fréchet equivalence, the approximation of monotone maps by homeomorphisms, Peano spaces, and a discussion of the topological index of maps into the plane. After a development of further ideas and tools from topology and measure theory, Radó addresses an essential question that equates two sorts of areas for surfaces represented by maps of a 2cell or a 2sphere into 3space. Readership Graduate students and research mathematicians interested in geometry and topology. Table of Contents  Background material
 Curves and surfaces
 Arc length and related topics
 Plane tranformations
 Surface area
 Bibliography
 Index
