Abstract: A measurable function f is said to be in L1(R) if ∫ |f| < ∞. These functions play an important role in analysis. We show that any function in L1(R) can be approximated by a continuous function in the L1 norm. More precisely, for any L1(R) function f, given ? > 0 there exists a continuous function g in L1(R) such that the L1 norm of (f-g) is less than ?. We present a proof of this fact, along with a running example to illustrate the concepts of the proof. The talk concludes with an application which sets the stage for the November 14th seminar.