Problem 5: Let \(\{a_n\}\) be a sequence of non-negative numbers. Let \(E = [0, \infty)\) and define
\(f(x) = a_n\), \(x \in [n, n+1)\), \(n = 1, 2, ...\)
Show that
\(\int_E f = \sum_{n=1}^\infty a_n\).
That is, any series of non-negative terms can be represented as a Lebesgue integral.