Abstract of Colloquium talk at Math Department of WVU, April 17, 1997

Professor Udayan B. Darji

University of Louisville, Louisville, Kentucky

Extensions Which Preserve Derivate Structures


In this talk we present two very general theorems from which a classical theorem of Lusin and a classical theorem of Petruska and Laczkovich follow readily. Our theorems are also very useful for constructing pathological examples. For instance, as a simple application of these theorems we can obtain continuous nowhere monotone functions of bounded variation which have derivative zero ae. We will also show how characterizations of certain exceptional sets follow from these theorems as well.