The representation of interior algebras by preorder fields can be generalized to a representation theorem for arbitrary ( normal ) Boolean algebras with operators.
32.
The Riesz representation theorem relies fundamentally not just on the presence of an inner product, but also on the completeness of the space.
In these more general contexts, the bracket does not have the meaning of an inner product, because the Riesz representation theorem does not apply.
36.
The Riesz representation theorem states that " every " element of " H * " can be written uniquely in this form.
37.
By the Riesz representation theorem, the continuous dual of a Hilbert space is again a Hilbert space which is anti-isomorphic to the original space.
38.
Typical examples of distributive lattice are totally ordered sets, isomorphic to a lattice of sets, ordered by inclusion ( Birkhoff's representation theorem ).
39.
*PM : Wagner-Preston representation theorem, id = 8275 new !-- WP guess : Wagner-Preston representation theorem-- Status:
40.
*PM : Wagner-Preston representation theorem, id = 8275 new !-- WP guess : Wagner-Preston representation theorem-- Status:
