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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2014 • Question 5

Question

Math 6210 • Real Analysis Fall 2014 • Question 5

Let \(A\subset \mathbb R\) and \(A+A\) denote \(\{a_1+a_2:\ a_1,a_2\in A\}\). Show that if \(\lambda (A^c)=0\) then \(A+A=\mathbb R\).

Raw LaTeX

Let \(A\subset\mathbb R\) and \(A+A\) denote
\(\{a_1+a_2:\ a_1,a_2\in A\}\). Show that if \(\lambda(A^c)=0\) then
\(A+A=\mathbb R\).

Topic Tags

Lebesgue Measure and Translation Invariance