Let \(f\) be integrable on \(\mathbb R\) with respect to Lebesgue measure, and define \[ F(x)=\int _{-\infty }^{x} f(t)\,dt \] Prove that \(F\) is continuous.
Question
Math 6210 • Real Analysis
Fall 2007 • Question 1
Question
Fall 2007 • Question 1
Let \(f\) be integrable on \(\mathbb R\) with respect to Lebesgue measure, and define \[ F(x)=\int _{-\infty }^{x} f(t)\,dt \] Prove that \(F\) is continuous.