Measure Theory (graduate Texts In Mathematics Vol. 18)

P.R. Halmos __Measure Theory__ __"As with the first edition, this considerably improved volume will serve the interested student to find his way to active and creative work in the field of Hilbert space theory."—__MATHEMATICAL REVIEWS 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 sour ce of refer ence for the more advanced mathematician. I have tried to keep to a minimum the amount of new and unusual terminology and notation. In the few pI aces where my nomenclature differs from that in the existing literature of meas ure 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." The only necessary prerequisite for an intelligent reading of the first seven chapters of this book is what is known in the Uni ted States as undergraduate algebra and analysis. For the convenience of the reader, {sect} 0 is devoted to a detailed listing of exactly what knowledge is assumed in the various chapters Useful both as a text for students and as a source of reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory which is most useful for its application in modern analysis. Topics studied include sets and classes, measures and outer measures, measurable functions, integration, general set functions, product spaces, transformations, probability, locally compact spaces, Haar measure and measure and topology in groups. The text is suitable for the beginning graduate student as well as the advanced undergraduate. Front Matter....Pages i-xi Prerequisites....Pages 1-8 Sets and Classes....Pages 9-29 Measures and Outer Measures....Pages 30-48 Extension of Measures....Pages 49-72 Measurable Functions....Pages 73-94 Integration....Pages 95-116 General Set Functions....Pages 117-136 Product Spaces....Pages 137-160 Transformations and Functions....Pages 161-183 Probability....Pages 184-215 Locally Compact Spaces....Pages 216-249 Haar Measure....Pages 250-265 Measure and Topology in Groups....Pages 266-289 Back Matter....Pages 291-304 Useful as a text for students and a reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory most useful for its application in modern analysis. Coverage includes sets and classes, measures and outer measures, Haar measure and measure and topology in groups. From the reviews:'Will serve the interested student to find his way to active and creative work in the field of Hilbert space theory.'--MATHEMATICAL REVIEWS Useful As A Text For Students And A Reference For The More Advanced Mathematician, This Book Presents A Unified Treatment Of That Part Of Measure Theory Most Useful For Its Application In Modern Analysis. Coverage Includes Sets And Classes, Measures And Outer Measures, Haar Measure And Measure And Topology In Groups. From The Reviews: Will Serve The Interested Student To Find His Way To Active And Creative Work In The Field Of Hilbert Space Theory. --mathematical Reviews Sets And Classes -- Measures And Outer Measures -- Extension Of Measures -- Measurable Functions -- Integration -- General Set Functions -- Product Spaces -- Transformations And Functions -- Probability -- Locally Compact Spaces -- Haar Measure -- Measure And Topology In Groups. [by] Paul R. Halmos. Reprint Of The Ed. Published By Van Nostrand, New York, In Series: The University Series In Higher Mathematics. Bibliography: P. 293-296. P.R. Halmos Measure Theory "As with the first edition, this considerably improved volume will serve the interested student to find his way to active and creative work in the field of Hilbert space theory."— MATHEMATICAL REVIEWS