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Measureandintegral

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AnalysisIInstructor:RussellBrown

MWF2-2:50pmOffice:POT741

CB347Phone:8592573951

Spring2007**************

Officehours:M3–4,Mathskeller

WF11–12,POT741

andbyappointment.

Text:Measureandintegral,R.WheedenandA.Zygmund.

ThiscoursewillintroducestudentstoLebesgueintegration.Thecontentofthis

coursewillbeexaminedintherealanalysisportionoftheanalysispreliminary

examination.

Homework:Youshouldendeavortowriteoutyourhomeworkclearly.Use

completesentences.Givespecificreferencestofactsfromlectureorthetext.Itwill

notbeacceptabletogiveareferencesuchas“IheardthatNickKirbysaiditwas

true.”Notethathomeworkisasubstantialfractionofyourgrade.

Thehomeworkwillbeoftwotypes.Exerciseswhicharemoreroutineandwill

generallynotbecollected.Problemswillbemoreinterestingandwillbecollected

andgraded.

Wewillscheduletworecitationsectionswherehomeworkexerciseswillbediscussed.

Beawarethatyourinstructorisoldandcranky.Latehomeworkwillnotbe

accepted.Youmayonlywriteononesideofeachsheetofpaper.Leavegenerous

margins.Imayusethemarginsandthebackofeachsheetforcomments.Iprefer

thatyoursolutionsbehandwritten.

Lecturenotes:Studentswillbeaskedtopreparelecturenotesfortheclass.Each

studentwillbeaskedtopreparelecturenotesforreviewbymeandthen

distributiontotheclass.Wewillrotatethroughtheclassalphabetically.Students

areencouragedtotakenotesforeverylecture.

Grading:Yourgradewillbedeterminedasfollows.Lecturenotes53

Participationinrecitation47

Homework197

Exam206

Final297

Total800

Exams:Therewillbeonemidtermexamandafinal.Thefinalwillbe

cumulative.Thefinalexamisat3:30-5:30pmonWednesday,May2,2007,

Anumberofothertextbookscoverthematerialofthiscourse.Three1ofmy

favoritesare:

1Thisremindsmeofajoke:Therearethreekindsofmathematicians,thosewhoknowhowtocountandthosewhodon’t.•LebesgueintegrationonEuclideanspaces,BFJones.

•RealAnalysis,H.Royden

•RealandComplexAnalysis,W.Rudin.

•Inequalities,Hardy,LittlewoodandPolya.

•Realanalysis,measuretheoryandHilbertspaces,E.M.SteinandRami

Shakarchi.

•Analysis,E.LiebandM.Loss.

Schedule:IhopetocoverChapters1to7ofWheedenandZygmund.Belowisa

tentativeschedule.Itwillbeamusingtoseeifwecanfollowit.ChapterTopicsDates

1Preliminaries1/8–1/14

2FunctionsofboundedvariationandtheRiemann–

Stieltjesintegral1/16–2/4

3Lebesguemeasureandoutermeasure2/6–2/20

Exam2/23(tentative)

4Measurablefunctions2/25–3/8

5TheLebesgueintegral3/18–4/1

6Repeatedintegration4/3–4/17

7Differentiation4/19–4/27.

January9,2007