Função de Variação Limitada

Abstract

The limitedvariationfunctionsareaspecialclassoffunctionswithfinitevariationinFora continuous functionofasinglevariable,beingoflimitedvariation,thelengthtraveledby f (x) when x is afiniteintervalhasafinitevalue.Throughoutthiswork,wepresentsomeconcepts and resultsrelatedtofunctions,aimingtoestablishtheadequatebasisfordiscussinglimited variationfunctions.Themainpurposeofthisworkistopresentsometypesoflimitedvariation functions. Inthefirstchapterwepresentbasicconceptsoffinite,infiniteandlimitedsetand some propertiesthatwewillusethroughoutthiswork.Inthesecondchapter,weinitiallymadea succinct approachtotopologyontheline,aimingatEstablishabasisfordevelopingsubsequent content. Next,westudysomepropertiesoffunctions.Thethirdchapterisdevotedtostudying the studyoffunctionintegralsusingtheRiemannsumandpresentinginterestingpropertiesabout integrablefunctions.Finally,inthefourthchapter,wepresentthefunctionsoflimitedvariation and we show some examples.