Word Count : 296

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We are asked to verify Fatou’s lemma for the sequence of functions [ f_n(x) = \begin{cases} 2n, & x \in \left(\frac{1}{2n}, \frac{1}{n}\right) [2mm] 0, & x \in \left(0, \frac{1}{2n}\right] \cup \left[\frac{1}{n}, 1\right] \end{cases} ] on the interval ([0,1]) with the Lebesgue measure. Let's go step by step. --- Step ____ ______ __________ __________ _____ _________ _________ _________ _________ ___.
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