Given a continuous function $f:\mathbb{R}^n \to\mathbb{R}$ with $M_f(x,r)=\frac{\sup_{|x-y|\le r}|f(x)-f(y)|}r$, the so-called ``Big Lip" and ``Little Lip" functions are defined as follows:
$Lip \ f(x)=\limsup_{r\to 0^+}M_f(x,r)$ $lip \ f(x)=\liminf_{r\to 0^+}M_f(x,r)$
The Rademacher-Stepanov Theorem tells us that $f$ is differentiable almost everywhere on $L_f=\{x \,|\,Lip \ f(x)<\infty\}$. On the other hand, as Balogh and Csörnyei showed, this theorem no longer holds if we replace $L_f$ with $l_f=\{x \,|\,lip\ f(x)<\infty\}$. In this talk, I consider the problems of characterizing the sets $E\subset\mathbb{R}$ for which there exist a continuous function $f$ such that $l_f=E$ as well as characterizing the sets of non-differentiability for functions $f$ with $l_f=\mathbb{R}$. I will also examine some additional questions about the relationship between $L_f$ and $l_f$.