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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Summer 2016 • Question 2

Question

Math 6210 • Real Analysis Summer 2016 • Question 2

If \(f:\mathbb R\to \mathbb R\) is Lipschitz and \(A\) is \(\lambda \)-measurable, then \(f(A)\) is measurable. Recall that a function is Lipschitz if there exists \(C\) so that \[ d(f(x),f(y))\le C\,d(x,y) \] for all \(x,y\in \mathbb R\).

Raw LaTeX

If \(f:\mathbb R\to\mathbb R\) is Lipschitz and \(A\) is
\(\lambda\)-measurable, then \(f(A)\) is measurable. Recall that a function is
Lipschitz if there exists \(C\) so that
\[
d(f(x),f(y))\le C\,d(x,y)
\]
for all \(x,y\in\mathbb R\).

Topic Tags

Measurable Functions