8.14 Let 1≤p<[infinity]. For t∈[0,1], let x 1
​
(t)=1, x 2
​
(t)={ 1,
−1,
​
if 0≤t≤1/2
if 1/2 ​
and for n=1,2,…,j=1,…,2 n
, x 2 n
+j
​
(t)= ⎩
⎨
⎧
​
2 n/p
,
−2 n/p
,
0,
​
if (2j−2)/2 n+1
≤t≤(2j−1)/2 n+1
if (2j−1)/2 n+1
otherwise. ​
Then the Haar system {x 1
​
,x 2
​
,x 3
​
,…} is a Schauder basis for L p
([0,1]). Each x n
​
is a step function.