Analysis tools with application【Bruce K. Driver】

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1、BruceK.DriverAnalysisToolswithApplications,SPINSpringer’sinternalprojectnumber,ifknownJune9,2003File:analpde.texSpringerBerlinHeidelbergNewYorkHongKongLondonMilanParisTokyoContentsPartIBasicTopological,MetricandBanachSpaceNotions1Limits,sums,andotherbasics.............................31.1SetOperat

2、ions..........................................31.2Limits,Limsups,andLiminfs.............................41.3Sumsofpositivefunctions................................61.4Sumsofcomplexfunctions................................101.5Iteratedsums...........................................131.6cp—spaces,Mi

3、nkowskiandHolderInequalities..............151.6.1Someinequalities..................................151.7Exercises..............................................191.7.1SetTheory.......................................191.7.2LimitProblems...................................201.7.3DominatedConvergenceTh

4、eoremProblems..........211.7.4Inequalities.......................................222Metric,BanachandTopologicalSpaces....................252.1Basicmetricspacenotions................................252.2Continuity..............................................272.3BasicTopologicalNotions............

5、....................292.4Completeness...........................................352.5BoundedLinearOperatorsBasics.........................372.6CompactnessinMetricSpaces............................412.7CompactnessinFunctionSpaces..........................482.8Connectedness..........................

6、................502.9Supplement:SumsinBanachSpaces.......................532.10WordofCaution........................................542.10.1RiemannianMetrics...............................552.11Exercises...............................................562.11.1BanachSpaceProblems.....................

7、.......582.11.2Ascoli-ArzelaTheoremProblems....................594Contents2.11.3GeneralTopologicalSpaceProblems.................602.11.4ConnectednessProblems...........................603LocallyCompactHausdorffSpa