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**11 - 14**of**14**### Easy Proofs of Some Consequences of Gleason's Theorem

"... The famous Gleason's Theorem gives a characterization of measures on lattices of subspaces of Hilbert spaces. While the proof of Gleason's Theorem is higly advanced, some of its consequences, in particular the nonexistence of hidden variables (=two-valued states), can be proved relatively easily ..."

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The famous Gleason's Theorem gives a characterization of measures on lattices of subspaces of Hilbert spaces. While the proof of Gleason's Theorem is higly advanced, some of its consequences, in particular the nonexistence of hidden variables (=two-valued states), can be proved relatively easily. Here we present some of such results.

### Piron's and Bell's Geometrical Lemmas

, 2001

"... The famous Gleason's Theorem gives a characterization of measures on lattices of subspaces of Hilbert spaces. The attempts to simplify its proof lead to geometrical lemmas that possess also easy proofs of some consequences of Gleason's Theorem. We contribute to these results by solving two open ..."

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The famous Gleason's Theorem gives a characterization of measures on lattices of subspaces of Hilbert spaces. The attempts to simplify its proof lead to geometrical lemmas that possess also easy proofs of some consequences of Gleason's Theorem. We contribute to these results by solving two open problems formulated by Chevalier, Dvurecenskij and Svozil. Besides, our use of orthoideals provides a unified approach to finite and infinite measures.

### Geometry and Information Retrieval

"... With the arrival of the digital computer in the second half of the twentieth century, a vast amount of information has been stored and made available. The growing of accesible information has reached an exponential growing rate, and computer scientists have been worried about the problem of accessin ..."

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With the arrival of the digital computer in the second half of the twentieth century, a vast amount of information has been stored and made available. The growing of accesible information has reached an exponential growing rate, and computer scientists have been worried about the problem of accessing and searching this information accurately. The subfield of Computer Science that deals with the representation, automated storage and retrieval of information items is called information retrieval (IR) [10], [1], [12]. We denote these items as documents (unit of retrieval) which might be a paragraph, a section, a chapter, a web page, an article, or a whole book [1]. The two main views of an IR system are the following. The former, the indexing subsystem, which takes a set of documents and converts them to a suitable representation (what is called an index), and the latter (the most important one) retrieval subsystem which