请帮我翻译此数学摘要（英文）关于可测函
ConvergencesofmeasurablefunctionsDirectedbyProfessorLingZhang(如果zhang是姓) (或者改成realvariablefunctions)。 Inthispaper,wemainlydiscussthenotionsofeverywhereconvergent,uniformlyconvergent,almosteverywhereconvergent,almostconvergent,(我猜这儿不是分号)convergentinmeasureandtheirrelations。 Thispaperisseparatedin...全部
ConvergencesofmeasurablefunctionsDirectedbyProfessorLingZhang(如果zhang是姓) (或者改成realvariablefunctions)。
Inthispaper,wemainlydiscussthenotionsofeverywhereconvergent,uniformlyconvergent,almosteverywhereconvergent,almostconvergent,(我猜这儿不是分号)convergentinmeasureandtheirrelations。
Thispaperisseparatedinto ,MainResults,CounterexamplesandApplications。Thesecondpartincludes5theorems,andstudiestherelationsamongalmosteverywhereconvergent,almostuniformlyconvergentandalmostconvergent;therelationsamongalmostuniformlyconvergent,almostconvergentandconvergentinmeasure;therelationsbetweenconvergentinmeasureandalmosteverywhereconvergent。
Wealsodiscusstheeffectsifwemodifytheconditionsofthetheoremsandgivecounterexamplesafterwards。Inthelastsection,wegiveseveralapplicationsthevariousconvergencesforthemeasurablefunctions,andexemplifytheimportanceofconvergencesofmeasurablefunctionsandtheirrelationsinthestudyofrealanalysis。
,relations,counterexample,applications。(后面这三个词放到关键词里一般不合适)。收起
