basic analysis - k. kuttler

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1、BasicAnalysisKennethKuttlerApril16,20012Contents1BasicSettheory91.1Exercises...............................................101.2TheSchroderBernsteintheorem..................................111.3Exercises...............................................142LinearAlgebra152.1VectorSpaces

2、.............................................152.2LinearTransformations.......................................182.3Innerproductspaces.........................................222.4Exercises...............................................302.5Determinants...............................

3、..............312.6Thecharacteristicpolynomial....................................382.7Therankofamatrix.........................................402.8Exercises...............................................413Generaltopology433.1Compactnessinmetricspace...............................

4、.....493.2Connectedsets............................................523.3TheTychonotheorem.......................................553.4Exercises...............................................574SpacesofContinuousFunctions614.1Compactnessinspacesofcontinuousfunctions..................

5、........614.2StoneWeierstrasstheorem......................................634.3Exercises...............................................675AbstractmeasureandIntegration715.1Algebras...............................................715.2Monotoneclassesandalgebras........................

6、...........715.3Exercises...............................................785.4TheAbstractLebesgueIntegral...................................805.5ThespaceL1.............................................835.6Doublesumsofnonnegativeterms.................................875.7Vitaliconverg

7、encetheorem.....................................885.8Theergodictheorem.........................................905.9Exercises...............................................9534CONTENTS6TheConstructionOfMeasures976.1Outermeasures............................................976.2Positi

8、velinearfunctionals