The microubundle representation theorem

The Riesz representation theorem

Representation Theorem for Stacks

In this paper i is a natural number and x is a set. Let A be a set and let s1, s2 be finite sequences of elements of A. Then s1s2 is an element of A∗. Let A be a set, let i be a natural number, and let s be a finite sequence of elements of A. Then s i is an element of A∗. The following two propositions are true: (1) ∅ i = ∅. (2) Let D be a non empty set and s be a finite sequence of elements of...

Hyperseparoids: A Representation Theorem

In this note, hyperseparoids are introduced; hyperseparoids are to separoids as Tverberg’s theorem is to Radon’s theorem. Also, a geometric representation theorem for acyclic kseparoids is presented which generalises that for separoids exhibited in [2].

Martingale Representation Theorem for the G-expectation

This paper considers the nonlinear theory of G-martingales as introduced by Peng in [16, 17]. A martingale representation theorem for this theory is proved by using the techniques and the results established in [20] for the second order stochastic target problems and the second order backward stochastic differential equations. In particular, this representation provides a hedging strategy in a ...

The Stone Representation Theorem for Boolean Algebras

The Stone Representation Theorem for Boolean Algebras, first proved by M. H. Stone in 1936 ([4]), states that every Boolean algebra is isomorphic to a field of sets. This paper motivates and presents a proof.