Lebesgue Spaces Flashcards
Define a normed linear space
Define a Cauchy sequence
Define a Banach space
Define a Lebesque space
When are the limit of two sequences of measurable functions equivelent?
Define conjugate exponents
State Young’s inequality
State Holder’s inequality
State Minkowski’s inequality
If q > p is L^q(E) in L^p(E)?
State the Riesz Fischer Theorem
Define essentially bounded
Define L infinity and its nrom
When does a sequence of functions converge in L^infinity
Define Dense
The subspace of simple functions is
Are the step functions dense?
Define seperable
Is L^p(E) separable?
Are cts functions dense?
Is L^\infty seperable
Define a linear functional
Define a bounded linear functional
Give the norm of a functional in terms of sup
Define the dual space
If two functionals agree on a dense subset then
State Reisz Representation Theorem
