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Ioannis Tsokanos
Ioannis Tsokanos
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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. For the proof of L+L=R see the paper of Erdős.

The set L of all Liouville numbers is an 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. For the proof of L+L=R see the paper of Erdős.

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. For the proof of L+L=R see the paper of Erdős.

Source Link
Ioannis Tsokanos
Ioannis Tsokanos
  • 11
  • 2

The set L of all Liouville numbers is an 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. For the proof of L+L=R see the paper of Erdős.