Determine whether the following statements are true or false. If it is false, explain why please. iff belongs to L, then f belongs to L. 1. 2. If , be the Lebesgue measure on Rand Eis an open subset of R. then ,(E) > Oif and only if Eis nonempty. 3. F(X, 6, #) is a measure space and X = {E € 6: (E)=0}, then X is a 6-algebra. 4. ifbe the Lebesgue measure on Rand Eis a Borel subset of R, then 1(E) > Oif and only if Eis nonempty. 5. If 41 --> Hm are measures on G and al,..., On are nonnegative real numbers, then the function , defined for E E G by (E) =;;(E) is a measure on G.