Question: Please answer the question in the picture below. This is related to Lebesgue Integration in Measure Theory. Please refer to the book Lebesgue Measure and

Please answer the question in the picture below. This is related to Lebesgue Integration in Measure Theory. Please refer to the book Lebesgue Measure and Integration An Introduction by Frank Burk Chapter 5.

1. Let f : [0, 1] -> R be defined by if r E C f(x) = 1 0 if x E [0, 1] \\ C, where C is the (usual) Cantor set in [0, 1]. For each n E N, construct a step function Un such that f

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