What can be said about the Lebesgue integral of the function in the interval $[0,1]$ defined as $$f(x)= \begin{cases}9^n, x\in\mathbb{Q}^c\\0, \:x\in\mathbb{Q}\end{cases}$$ where $n$ is the number of zeroes immediately after decimal point. I think the answer is 1, but am unable to justify it. I...