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.

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