Measure of a non-negative measurable function

Question

Please refer to the question and my work in the image found at: drive[DOT]google.com/file/d/1-rDCuYfuM8eqC5TwI7jegK9QpncAFf6l/view?usp=drivesdk

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Answer 1

\lim_{n \to \infty} \int_X s_n \, d\mu = \int_X f \, d\mu.