Question: This is from functional analysis and Lebesgue measurable function from measure theory. I am not satisfied with the answer someone provided before. 1. Let {

This is from functional analysis and Lebesgue measurable function from measure theory. I am not satisfied with the answer someone provided before.

1. Let { 71, 12,...} be any enumeration of Q, and let fx : R - R be defined by fk () = 1 if re {n1, 12, .... TK) if r ER {(1, 12, ..., rk). (a) Calculate f, and fk. (b) Calculate lim inf fx and lim sup fk. (c) Calculate limk-+co fk

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