测度论

Mymainpurposeinthisbookistopresentaunifiedtreatmentofthatpartofmeasuretheorywhichinrecentyearshasshownitselftobemostusefulforitsapplicationsinmodernanalysis.IfIhaveaccomplishedmypurpose,thenthebookshouldbefoundusablebothasatextforstudentsandasasourceofreferenceforthemoreadvancedmathematician.Ihavetriedtokeeptoaminimumtheamountofnewandunusualterminologyandnotation.Inthefewplaceswheremynomenclaturediffersfromthatintheexistingliteratureofmeasuretheory,Iwasmotivatedbyanattempttoharmonizewiththeusageofotherpartsofmathematics.Thereare,forinstance,soundalgebraicreasonsforusingtheterms"lattice"and"ring"forcertainclassesofsets--reasonswhicharemorecogentthanthesimilaritiesthatcausedHausdorfftouse"ring"and"field."