Aproximarea functionalelor liniare

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Deoarece Rn(p2n−1) = 0 (căci d = 2n − 1), avem succesiv
|Rn(f)|=|Rn(f − p2n−1)|
b
= [f(t) − p2n−1(f; t)]w(t)dt −
a
k=1
b
n
≤ |f(t) − p2n−1(f; t)|w(t)dt +
a
k=1
b
≤f(·) − p2n−1(f; ·)∞ w(t)dt +
a
n
wk[f(tk) − p2n−1(f; tk)]
wk|f(tk) − p2n−1(f; tk)|
n
k=1
wk
.