Question

Using the Dominated Convergence Theorem show that if f is an integrable function on $\mathbb{R}^d$, there exists a sequence $\left \{ f_n \right \}$ of measurable functions s.t. each $f_n$ is bounded and has support on a set of finite measure, and $\int \left | f_n-f \right |\rightarrow 0$ as $n$ goes to $\infty$.

Answer 1

"Since f_n is bounded