Show E-E contains an interval when m(E)>0 in Lebesgue measure

[Funky1981]

Homework Statement

Let (R,M,m) be Lebesgue measure space in R. Given E contained in R with m(E)>0 show that the set
E-E defined by

E-E:={x in R s.t. exists a, b in E with x= a-b }

contains an interval centered at the origin

Homework Equations

try to prove by contradiction and use the fact that for every a in (0,1) there exists an interval I s.t. m(E∩ I)>am(I)

 

[jbunniii]

What have you tried?