Hello!

can someone help me to prove this

Let A*B={a*b;a,b>0 a is element of A,b element of B.Prove that:

inf(AB)=inf(A)inf(B)

sup(AB)=sup(A)sup(B)

i've done the proof with inf(A+B)= inf (A) + inf(B) and inf(-A)= -inf(A) but i can't prove the problem above