ABSTRACT
In this chapter, the author now begins a series of investigations into the construction of an important subset called the Cantor Set. He follows a great series of homework exercises outlined, without solutions, in a really hard but extraordinarily useful classical analysis text by Stromberg. The author now proves additional interesting results that arise from the use of generalized Cantor sets via a series of exercises that readers complete. He shows the function is of great importance in developing a better understanding of measures. The author concludes that in this case, even though the two functions were equal a.e. with respect to Borel measure, only one was Borel measurable.
