# Thread: Let m be Lebesgue measure on the real line, and suppose that A and B are measurable

1. ## Let m be Lebesgue measure on the real line, and suppose that A and B are measurable

Hi everyone,
Let m be Lebesgue measure on the real line, and suppose that A and B are measurable subsets of the closed interval [0,1]. how do you show that if m(A)=m(B)=1, then m(A∩B)=1

2. Originally Posted by Kelles
Let m be Lebesgue measure on the real line, and suppose that A and B are measurable subsets of the closed interval [0,1]. how do you show that if m(A)=m(B)=1, then m(A∩B)=1
m(A) + m(B) = m(A∪B) + m(A∩B)