Hello, I am stuck with the following problem.

Let \Omega be the unit square \Omega=\{(x,y):0<x,y \leq 1\}, let \mathcal{F} be the class of sets of the form \{(x,y): x \in A, 0 < y \leq 1\}, where A \in \mathcal{B}.
( \mathcal{B}=\sigma(\mathcal{B}_0) and \mathcal{B}_0 is the class of finite disjoint unions of subintervals of (0,1] augmented by the empty set). Let P=\lambda(A) at this set(for a subinterval  I=(a,b] of (0,1], \lambda(I)=|I|=b-a). Show that (\Omega,\mathcal{F},P) is a probability measure space. Show that for A=\{(x,y):0<x \leq 1, y=1/2 \} that P_*(A) = 0 and  P^*(A) = 1 ( P^* is the outer measure of P and P_* is the inner measure of P)

Thanks in advance,