Exercise 3.3.3

Question

Compare Proposition 3.3.3 with Example 1.2.8. Can you now explain why the interchange of limits in Example 1.2.8 led to a false statement, whereas the interchange of limits in Proposition 3.3.3 is justified?

Prakash Anand · Accepted Answer

You cannot change the limits in Example 1.2.8 because the sequence of functions $f^{(n)}=x^{n}$ does not converge uniformly on $[0,1]$, and hence does not contradict \href{./exercise_3-3-2}{Proposition 3.3.3}.

Exercise 3.3.3

Answers

Comments

Exercise 3.3.3

Answers

Comments

Add answer