Continuity of Borel measurable Gleason frame functions - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T01:12:18Z http://mathoverflow.net/feeds/question/64492 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/64492/continuity-of-borel-measurable-gleason-frame-functions Continuity of Borel measurable Gleason frame functions Greg W Anderson 2011-05-10T11:59:24Z 2012-10-17T05:22:00Z <p>Gleason's theorem (Journal of Mathematics and Mechanics, Vol. 6, No. 6, 1957) classifies measures on the closed subspaces of a separable Hilbert space. A key lemma toward the proof of the theorem asserts the following. Let f be a nonnegative real-valued function on the 2-sphere in 3-space with the property that its sum on any triple of orthogonal points is independent of the triple. Then f is continuous. The question is whether the conclusion remains valid if one drops the nonnegativity assumption and assumes Borel measurability instead. </p> http://mathoverflow.net/questions/64492/continuity-of-borel-measurable-gleason-frame-functions/99387#99387 Answer by Valter Moretti for Continuity of Borel measurable Gleason frame functions Valter Moretti 2012-06-12T20:28:29Z 2012-06-12T20:28:29Z <p>Perhaps this could help <a href="http://arxiv.org/abs/1205.4504" rel="nofollow">http://arxiv.org/abs/1205.4504</a> bye W.</p>