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analysis

Source: miklos schweitzer 1994 q5

October 16, 2021

real analysisMeasure theory

Problem Statement

Let H be a

G_{\delta}

subset of

\mathbb R

whose closure has a positive Lebesgue measure. Prove that the set

H + H + H + H = \{ x + y + z + u : x , y , z , u \in H \}

contains an interval.