<p> <a href="http://www.golden-book.com/search/search.asp?key1=Graduate+Texts+in+Mathematics"><font color="#000066">Graduate Texts in Mathematics</font></a></p><p><span class="smallgray"><font color="#888888">Format:</font></span> Hardcover<br/><span class="smallgray"><font color="#888888">Publication Date:</font></span> June 1974<br/><span class="smallgray"><font color="#888888">Publisher:</font></span> Springer Verlag<br/><span class="smallgray"><font color="#888888">Dimensions:</font></span> 9.75"H x 6.5"W x 1"D; 1.3 lbs.<br/><span class="smallgray"><font color="#888888">ISBN-10:</font></span> 0387900888<br/><span class="smallgray"><font color="#888888">ISBN-13:</font></span> 9780387900889</p><p></p><p>Brief Introduction:</p><p><table cellspacing="5" cellpadding="0" width="100%" align="center" border="0"><tbody><tr><td valign="top" align="left" style="WIDTH: 98%; WORD-BREAK: break-all; WHITE-SPACE: normal;">My main purpose in this book is to present a unified treatment of that part of measure theory which in recent years has shown itself to be most useful for its applications in modern analysis. If I have accomplished my purpose, then the book should be found usable both as a text for students and as a source of reference for the more advanced mathematician. <br/>I have tried to keep to a minimum the amount of new and unusual terminology and notation. In the few places where my nomenclature differs from that in the existing literature of measure theory, I was motivated by an attempt to harmonize with the usage of other parts of mathematics. There are, for instance, sound algebraic reasons for using the terms "lattice" and "ring" for certain classes of sets--reasons which are more cogent than the similarities that caused Hausdorff to use "ring" and "field." </td></tr><tr><td class="neirongmulucss" valign="top" align="left"><font color="#ff6600"><strong><br/></strong></font></td></tr></tbody></table></p><p></p><p>Preface <br/>Acknowledgments <br/>SECTION <br/>  0 Prerequisites <br/>CHAPTER Ⅰ: SETS AND CLASSES <br/>  1 Set inclusion <br/>  2 Unions and intersections <br/>  3 Limits， complements， and differences <br/>  4 Rings and algebras <br/>  5 Generated rings and -rings <br/>  6 Monotone classes <br/>CHAPTER Ⅱ: MEASURES AND OUTER MEASUR. ES <br/>  7 Measure on rings <br/>  8 Measure on intervals <br/>  9 Properties of measures <br/>  10 Outer measures <br/>  11 Measurable sets <br/>CHAPTER Ⅲ: EXTENSION OF MEASURES <br/>  12 Properties of induced measures <br/>  13 Extension， completion， and approximation <br/>  14 Inner measures<br/>  15 Lebesgue measure<br/>  16 Non measurable cets<br/>CHAPTER Ⅳ: MEASURABLE FUNCTIONS<br/>  17 Measure spaces<br/>  18 Measurable functions<br/>  19 Combinations of measurable functions<br/>  20 Sequences of measurable functions<br/>  21 Pointwise convergence<br/>  22 Convergence in measure<br/>CHAPTER Ⅴ: INTEGRATION<br/>  23 Integrable simple functions<br/>  24 Sequences of integrable simple functions<br/>  25 Integrable functions<br/>  26 Sequences of integrable functions<br/>  27 Properties of Integrals<br/>CHAPTER Ⅵ: GENERAL SET FUNCTIONS<br/>  28 Signed measures<br/>  29 Hahn and Jordan decompostions<br/>  30 Absolute continuity<br/>  31 The Radon-Nikodym theorem<br/>  32 Derivatives of signed measures<br/>CHAPTER Ⅶ: PRODUCT SPACES<br/>CHAPTER Ⅷ: TRANSFORMATIONS AND FUNCTIONS<br/>CHAPTER Ⅸ: PROBABILITY<br/>CHAPTER Ⅹ: LOCALLY COMPACT SPACES<br/>CHAPTER Ⅺ: AHHR MEASURE<br/>CHAPTER Ⅻ: MEASURE AND TOPOLOGY IN GROUPS<br/>References<br/>Bibliography<br/>List of frequently used symbols<br/>Index</p><p> <br/></p>

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