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 N. notations) of fact that gn (x) → g (x) for each x E A. b) Does a) allow us to conclude that lim p In = Se g? If it is not the case, explain why? || E E

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.