Rudin Analysis book：shrink nicely

Let $\displaystyle m$ be the lebesgue measure on $\displaystyle R^k$, a signed measure $\displaystyle u$ is absolutely continous with respect to $\displaystyle m$,$\displaystyle f \in L^1(R^k)$ be the Radon-Nikodym derivative of $\displaystyle u$ with respect to $\displaystyle m$.

$\displaystyle x\in R^k$, and for any set sequence $\displaystyle \{E_i\}$ which shrink nicely to $\displaystyle x$, we have

$\displaystyle \limsup_{i\to \infty}\frac{u(E_i)}{m(E_i)}\leq f(x)$.

Prove that $\displaystyle -f$ is the Radon-Nikodym derivative of $\displaystyle -u$ with respect to $\displaystyle m$.

and show that $\displaystyle \liminf_{i\to \infty}\frac{u(E_i)}{m(E_i)}\geq f(x)$.

The Definition of "Shrink nicely" in Rudin's Real and Complex Analysis Book:

A sequence of measureable sets $\displaystyle {E_i}$ shrink nicely to x if there is a positive number $\displaystyle a$ and a sequence of Ball B(x,r_i) centered at $\displaystyle x$ with radias $\displaystyle r_i$ satisfying

(1)$\displaystyle E_i$ is contained in $\displaystyle B(x,r_i)$

(2)$\displaystyle \lim_{i\to \infty}r_i=0$

(3)$\displaystyle \left|u\right|(E_i)\geq am(B(x,r_i))$, for all i=1,2,....

I have proved the first problem.

for the second problem, Completely don't know where to start, Please help me out. Appreciation more than I can say!