Length and area
Author(s)
Bibliographic Information
Length and area
（Colloquium publications / American Mathematical Society, v. 30）
American Mathematical Society, 1948
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Note
Includes bibliographical references (p. 562-569) and index
Description and Table of Contents
Description
Rado's colloquium is a systematic treatment of Lebesgue theory, with an emphasis on the work of Morrey and of Rado 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 Frechet 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, Rado addresses an essential question that equates two sorts of areas for surfaces represented by maps of a 2-cell or a 2-sphere into 3-space.
Table of Contents
Background material Curves and surfaces Arc length and related topics Plane tranformations Surface area Bibliography Index.
by "Nielsen BookData"