$\displaystyle (X,F,\mu)=([-1,1],\Lambda,\lambda)$ , where $\displaystyle \Lambda$ is a sigma algebra of Lebesgue measurable sets and $\displaystyle \lambda$ is Lebesgue measure. Define $\displaystyle v(A)= \int_A x d\lambda$ for all$\displaystyle A \in \Lambda$.

a) prove $\displaystyle v$ is a signed measure.

b) prove $\displaystyle v << \lambda$

c)Find the Hahn-Jordan decomposition of $\displaystyle v$ and its total variation.

i dont even know how to get start. please help me. and im not sure what << means on b).