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For a general Lp space: In the notation of Lp norms:
Let f and g be Lp functions, then:
f+gp <= fp+gp
Specifically for p=2, using integrals, we have (where "S" means integral):
(S(f+g)2)1/2 <= (S(f)2)1/2+(S(g)2)1/2
and again, replacing p with 2 will yield the definition is a general Lp space.
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