gtm 180-srivastava s.m___a course on borel sets (springer 1998)

《gtm 180-srivastava s.m___a course on borel sets (springer 1998)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、ACourseonBorelSetsS.M.SrivastavaSpringerAcknowledgmentsIamgratefultomanypeoplewhohavesuggestedimprovementsintheoriginalmanuscriptforthisbook.InparticularIwouldliketothankS.C.Bagchi,R.Barua,S.Gangopadhyay(n´eeBhattacharya),J.K.Ghosh,M.G.Nadkarni,andB.V.Rao.Mydeepestfeelingsofgratitudean

2、dap-preciationarereservedforH.Sarbadhikariwhoverypatientlyreadseveralversionsofthisbookandhelpedinallpossiblewaystobringthebooktoitspresentform.ItisapleasuretorecordmyappreciationforA.MaitrawhoshowedthebeautyandpowerofBorelsetstoagenerationofIndianmathematiciansincludingme.Ialsothankhi

3、mforhissuggestionsduringtheplanningstageofthebook.IthankP.BandyopadhyaywhohelpedmeimmenselytosortoutalltheLATEXproblems.ThanksarealsoduetoR.KarforpreparingtheLATEXfilesfortheillustrationsinthebook.IamindebtedtoS.B.Rao,DirectoroftheIndianStatisticalInstituteforextendingexcellentmoralandm

4、aterialsupport.AllmycolleaguesintheStat–MathUnitalsolentamuchneededandinvaluablemoralsupportduringthelonganddifficultperiodthatthebookwaswritten.Ithankthemall.Itakethisopportunitytoexpressmysincerefeelingsofgratitudetomychildren,RosyandRavi,fortheirgreatunderstandingofthetaskItookontomys

5、elf.Whattheymissedduringtheperiodthebookwaswrittenwillbeknowntoonlythethreeofus.Finally,Ipayhomagetomylatewife,Kiranwhoreallyunderstoodwhatmathematicsmeanttome.S.M.SrivastavaContentsAcknowledgmentsviiIntroductionxiAboutThisBookxv1CardinalandOrdinalNumbers11.1CountableSets..............

6、...........11.2OrderofInfinity........................41.3TheAxiomofChoice......................71.4MoreonEquinumerosity....................111.5ArithmeticofCardinalNumbers...............131.6Well-OrderedSets.......................151.7TransfiniteInduction......................181.8Ordin

7、alNumbers........................211.9Alephs..............................241.10Trees...............................261.11InductiononTrees.......................291.12TheSouslinOperation.....................311.13IdempotenceoftheSouslinOperation............342TopologicalPreliminaries