<s>
In	O
mathematics	O
more	O
specifically	O
,	O
in	O
functional	B-Application
analysis	I-Application
and	O
numerical	B-General_Concept
analysis	I-General_Concept
Stechkin	B-Algorithm
's	I-Algorithm
lemma	I-Algorithm
is	O
a	O
result	O
about	O
the	O
ℓq	O
norm	O
of	O
the	O
tail	O
of	O
a	O
sequence	O
,	O
when	O
the	O
whole	O
sequence	O
is	O
known	O
to	O
have	O
finite	O
ℓp	O
norm	O
.	O
</s>
<s>
Here	O
,	O
the	O
term	O
"	O
tail	O
"	O
means	O
those	O
terms	O
in	O
the	O
sequence	O
that	O
are	O
not	O
among	O
the	O
N	O
largest	O
terms	O
,	O
for	O
an	O
arbitrary	O
natural	O
number	O
N	O
.	O
Stechkin	B-Algorithm
's	I-Algorithm
lemma	I-Algorithm
is	O
often	O
useful	O
when	O
analysing	B-Algorithm
best-N-term	O
approximations	O
to	O
functions	O
in	O
a	O
given	O
basis	O
of	O
a	O
function	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
Thus	O
,	O
Stechkin	B-Algorithm
's	I-Algorithm
lemma	I-Algorithm
controls	O
the	O
ℓq	O
norm	O
of	O
the	O
tail	O
of	O
the	O
sequence	O
(	O
and	O
hence	O
the	O
ℓq	O
norm	O
of	O
the	O
difference	O
between	O
the	O
sequence	O
and	O
its	O
approximation	O
using	O
its	O
largest	O
terms	O
)	O
in	O
terms	O
of	O
the	O
ℓp	O
norm	O
of	O
the	O
full	O
sequence	O
and	O
an	O
rate	O
of	O
decay	O
.	O
</s>
