Small sumsets in $\protect \mathbb{R}$: full continuous $3k-4$ theorem, critical sets
Small sumsets in $\protect \mathbb{R}$: full continuous $3k-4$ theorem, critical sets
We prove a full continuous Freiman's 3k-4 theorem for small sumsets in ℝ by using some ideas from Ruzsa's work on measure of sumsets in ℝ as well as some graphic representation of density functions of sets. We thereby get some structural properties of A, B and A+B when λ(A+B)<λ(A)+2λ(B) …