@InProceedings{Navara:AIP09, IS = { zkontrolovano 24 Feb 2011 }, UPDATE = { 2009-12-29 }, author = {Navara, Mirko}, title = {Mathematical questions related to non-existence of hidden variables}, year = {2009}, pages = {119-126}, booktitle = {Foundations of Probability and Physics - 5,}, editor = {L.~Accardi, G.~Adenier, C.~Fuchs, G.~Jaeger, A.Yu.~Khrennikov, J.-{\accent23 A}.~Larsson, S.~Stenholm (eds.)}, publisher = {American Institute of Physics}, address = {New York, USA}, issn = {0094-243X}, isbn = {978-0-7354-0636-0}, series = {AIP Conference Proceedings}, number = {1101}, book_pages = {400}, annote = {The famous Gleason's Theorem gives a characterization of states on lattices of subspaces of Hilbert spaces. The attempts to simplify its proof have led to easy proofs of some consequences, mainly the non-existence of hidden variables (dispersion-free states). Here we simplify some of them. We also formulate related open problems concerning spaces with rational coordinates and group-valued measures.}, keywords = {Gleason's Theorem, Bell inequalities, Bell's Geometrical Lemma, Piron's Geometrical Lemma, Hilbert space; hidden variable, dispersion-free state; two-valued state, Kochen--Specker theorem, group-valued measure}, edition = {1}, project = {GACR 201/07/1051}, psurl = {PDF}, }