2. Let {fn} be a sequence of nonnegative measurable functions and fn (x) → f (x) on a set A of finite measure and gn (x) = min (g (x) , fn (x)), where g is a bounded measurable which vanishes outside a set A. Moreover, g < f. a) Give a rigorous proof (using e and Ne notations) of fact that gn (x) → g (x) for each x E A. b) Does a) allow us to conclude that lim , In = Je 9? If it is not the case. explain why?

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