Example 8.1.7 (a): Pointwise Convergent Function Sequence
Let f_{n}(x) = max(n  n^{2} x  1/n, 0),
x [ 0, 1 ]. Show that
this sequence converges pointwise to the function f(x) = 0
for x [ 0, 1 ].
Recall that for each n the function
f_{n}(x) = max(n  n^{2} x  1/n, 0)
is piecewise linear:
Now take any > 0. Fix x [ 0, 1 ].

