Some additive properties of sets of real numbers

@article{Erds1981SomeAP,
  title={Some additive properties of sets of real numbers},
  author={Paul Erd{\"o}s and Kenneth Kunen and R. Daniel Mauldin},
  journal={Fundamenta Mathematicae},
  year={1981},
  volume={113},
  pages={187-199}
}
Some problems concerning the additive properties of subsets of R are investigated. From a result of G. G . Lorentz in additive number theory, we show that if P is a nonempty perfect subset of R, then there is a perfect set M with Lebesgue measure zero so that P+M = R. In contrast to this, it is shown that (1) if S is a subset of R is concentrated about a countable set C, then A(S+R) = 0, for every closed set P with A(P) = 0 ; (2) there are subsets G, and G s of R both of which are subspaces of… 
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