RealAnalysis

"Real Analysis" is the third volume in the "Princeton Lectures in Analysis" - a series of four textbooks. The aim of the series is to present the core areas of analysis in an integrated manner. This particular volume focuses on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. The book reflects the objectives of the series...

作者简介

"RealAnalysis"isthethirdvolumeinthe"PrincetonLecturesinAnalysis",aseriesoffourtextbooksthataimtopresent,inanintegratedmanner,thecoreareasofanalysis.Herethefocusisonthedevelopmentofmeasureandintegrationtheory,differentiationandintegration,Hilbertspaces,andHausdorffmeasureandfractals.Thisbookreflectstheobjectiveoftheseriesasawhole:tomakeplaintheorganicunitythatexistsbetweenthevariouspartsofthesubject,andtoillustratethewideapplicabilityofideasofanalysistootherfieldsofmathematicsandscience.Aftersettingforththebasicfactsofmeasuretheory,Lebesgueintegration,anddifferentiationonEuclidianspaces,theauthorsmovetotheelementsofHilbertspace,viatheL2theory.TheynextpresentbasicillustrationsoftheseconceptsfromFourieranalysis,partialdifferentialequations,andcomplexanalysis.Thefinalpartofthebookintroducesthereadertothefascinatingsubjectoffractional-dimensionalsets,includingHausdorffmeasure,self-replicatingsets,space-fillingcurves,andBesicovitchsets.Eachchapterhasaseriesofexercises,fromtherelativelyeasytothemorecomplex,thataretieddirectlytothetext.Asubstantialnumberofhintsencouragethereadertotakeoneventhemorechallengingexercises.Aswiththeothervolumesintheseries,"RealAnalysis"isaccessibletostudentsinterestedinsuchdiversedisciplinesasmathematics,physics,engineering,andfinance,atboththeundergraduateandgraduatelevels.