‖f‖
p
for f(x) = x
−1/3
on (0,1)
p =
1.5
The norm diverges as p → 3⁻. f ∈ L
p
iff 1 ≤ p < 3.
Mass concentrating: f
n
= n · 1
(0, 1/n)
on (0,1)
▶ Play
Reset
n =
5
f
n
→ 0 a.e. but ‖f
n
‖
1
= 1 for all n. The mass concentrates near 0.