A bipolar theorem for $L^0_+(\\Om, \\Cal F, \\P)$
A consequence of the Hahn-Banach theorem is the classical bipolar theorem which states that the bipolar of a subset of a locally convex vector pace equals its closed convex hull. The space $\\L$ of real-valued random variables on a proba...
W Brannath，W Schachermayer - SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business
A Bipolar Theorem for Subsets of L+0(Ω,σ,P)
We study the stability properties of heteroclinic cycles as they occur in heteroclinic networks on the tetrahedron. Their stability properties are investig...
W Brannath，W Schachermayer
A bipolar theorem for L_ + ^0 \\\\left( {\\\\Omega ,\\\\mathcal{F},\\\\mathbb{P}} ight)
In the course of the proof we show a decomposition lemma for convex subsets of \\\\\\\\(L_{^ + }^0 \\\\\\\\left( {\\\\\\\\Omega ,\\\\\\\\mathcal{F},\\\\\\\...
W Brannath，W Schachermayer - Springer Berlin Heidelberg
A bipolar theorem for L${}_+^0(\\Omega ,{\\cal F},{\\bf P})$
| ; . , (), p. 349-354 Full text | | Reviews | [B 97]. , , . (). [DS 94]. , , , (), — . | [HS 49]. , (), , , -.. | | [KS 97]. , , , Preprint (). [KPR 84]. , , , , (). | [M 74]. , , (). | [Me 79]. , , , (), — . | | [N 70]. , , , Nr. (),...
W Brannath，W Schachermayer
A bipolar theorem for $Lsp 0sb +(Omega,scr F,bold P)$.
| ; . , (), p. 349-354 Full text | | Reviews | [B 97]. , , . (). [DS 94]. , , , (), — . | [HS 49]. , (), , , -.. | | [KS 97]. , , , Preprint (). [KPR 84]. , , , , (). | [M 74]. , , (). | [Me 79]. , , , (), — . | | [N 70]. , , , Nr. (),...
W Brannath，W Schachermayer - 《Séminaire De Probabilités XXXIII》
Matrix Convexity: Operator Analogues of the Bipolar and Hahn–Banach Theorems ☆
Several basic results of convexity theory are generalized to the "quantized" matrix convex sets of Wittstock. These include the Bipolar theorem, a gauge ve...
EG Effros，S Winkler - 《Journal of Functional Analysis》
A Grothendieck representation for the completion of cones of continuous seminorms
O. Introduction Let (X, Y) be a locally convex linear topological space with topology Y and denote by C its cone of continuous seminorms. Then the two main results of this paper are a bipolar theorem for subsets of C and a Grothendieck-t...
W Ruess - 《Mathematische Annalen》
Bipolar Expansion of Screened Coulomb Potentials, Helmholtz' Solid Harmonics, and their Addition Theorems
The addition theorem for them and the bipolar expansion formula of a screened Coulomb potential are derived. A method for evaluating two‐center integrals ...
R Nozawa - 《Journal of Mathematical Physics》
A multidimensional bipolar theorem in ja:math
In this paper, we prove a multidimensional extension of the so-called Bipolar Theorem proved in Brannath and Schachermayer (S茅minaire de Probabilit茅s, vo...
B Bouchard，L Mazliak - 《Stochastic Processes & Their Applications》
