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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2015 • Question 4

Question

Math 6210 • Real Analysis Fall 2015 • Question 4

Let \(f\) be in \(L^1(\lambda ,\mathbb R)\). Show that for any \(r>0\) the function \[ h(s)=\int _{s-r}^{s+r} f\,d\lambda \] is continuous.

Raw LaTeX

Let \(f\) be in \(L^1(\lambda,\mathbb R)\). Show that for any \(r>0\)
the function
\[
h(s)=\int_{s-r}^{s+r} f\,d\lambda
\]
is continuous.

Topic Tags

Lebesgue Integration Lp Spaces and Sequence Spaces