6: Lebesgue Spaces

Question 1

L infinity is the collection of equivalence classes of ___ functions where f~g if there is F of measure 0 with f=g for x in F^c

Answer 1

essentially bounded

Question 2

a sequence of functions in L infinity converges to f iff there is G of measure 0 where the sequence converges to f ___ on E\G

Answer 2

uniformly

Question 3

the subspace of step functions in [a,b] is ___ in (Lp, ||.||)

Answer 3

dense

Question 4

a normed linear space is ___ if there exists a countable ___ subset in X

Answer 4

separable/dense

Question 5

if E is ___ then (Lp, ||.||) is separable

Answer 5

measurable

Question 6

___/___ functions are dense in (Lp, ||.||)

Answer 6

differentiable/smooth