Ajffsx

C 2C kf gk1 kfk1 kgk1 kk1 is a seminorm but not a norm kfk1 = 0 iff f(x) = 0 ae Deﬁnition L1(Rn) is the vector space of equivalence classes of integrable functions on Rn, where f is equivalent to g if f = g ae Then kk1 makes L1(Rn) into a normed vector space.

Ajffsx. Apr 13 11 ~(~r\,", ii ~ l'()u~'fv j ~ 't \10' j 7~ ~~ j i 111 superior court of wasidngton for king county the state of washington, v jon a. Simplest Case L1(Rn) The collection of integrable functions on Rn is a vector space Deﬁne kfk1 = Z jfj kcfk1 = jcjkfk1;.

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