| 书目名称 | Continuous Transformations in Analysis | | 副标题 | With an Introduction | | 编辑 | T. Rado,P. V. Reichelderfer | | 视频video | http://file.papertrans.cn/238/237027/237027.mp4 | | 丛书名称 | Grundlehren der mathematischen Wissenschaften | | 图书封面 |  | | 描述 | The general objective of this treatise is to give a systematic presenta tion of some of the topological and measure-theoretical foundations of the theory of real-valued functions of several real variables, with particular emphasis upon a line of thought initiated by BANACH, GEOCZE, LEBESGUE, TONELLI, and VITALI. To indicate a basic feature in this line of thought, let us consider a real-valued continuous function I(u) of the single real variable tt. Such a function may be thought of as defining a continuous translormation T under which x = 1 (u) is the image of u. About thirty years ago, BANACH and VITALI observed that the fundamental concepts of bounded variation, absolute continuity, and derivative admit of fruitful geometrical descriptions in terms of the transformation T: x = 1 (u) associated with the function 1 (u). They further noticed that these geometrical descriptions remain meaningful for a continuous transformation T in Euclidean n-space Rff, where T is given by a system of equations of the form 1-/(1 ff) X-I U, . . . ,tt ,. ", and n is an arbitrary positive integer. Accordingly, these geometrical descriptions can be used to define, for continuous transformations in Euc | | 出版日期 | Book 1955 | | 关键词 | Algebraic; Analysis; Continuous function; Topology; calculus; equation; function; variable | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-85989-2 | | isbn_softcover | 978-3-642-85991-5 | | isbn_ebook | 978-3-642-85989-2Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer-Verlag OHG. in Berlin, Göttingen and Heidelberg 1955 |
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