The set *L* of all Liouville numbers is an explicit example of a 0-dimensional Salem set such that its sum-set equals the whole real line, that is, *L*+*L*=*R*. Thus, 

> **dimF(*L*) = 0** and **dimF( *L*+*L*) =1**.

For the construction of a Rajchman measure over *L* see the paper of [Bluhm][1]. For the proof of *L*+*L*=*R* see the paper of [Erdős][2].


  [1]: https://www.ams.org/journals/proc/2000-128-09/S0002-9939-00-05276-X/S0002-9939-00-05276-X.pdf
  [2]: https://users.renyi.hu/~p_erdos/1962-18.pdf