Displaying similar documents to “The Bochner-Kolmogorov extension theorem for semispectral measures”

Projective limits of vector measures.

Fidel José Fernández y Fernández-Arroyo, Pedro Jiménez Guerra (1990)

Revista Matemática de la Universidad Complutense de Madrid

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A necessary and sufficient condition for the existence of the projective limit of measures with values in a locally convex space is given. A similar theorem for measures with values in different locally convex spaces (under certain conditions) is given too (in this case, the projective limit is valued in the projective limit of these spaces). Finally, a result about the projective limit of vector measures is stated.

Homography in ℝℙ

Roland Coghetto (2016)

Formalized Mathematics

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The real projective plane has been formalized in Isabelle/HOL by Timothy Makarios [13] and in Coq by Nicolas Magaud, Julien Narboux and Pascal Schreck [12]. Some definitions on the real projective spaces were introduced early in the Mizar Mathematical Library by Wojciech Leonczuk [9], Krzysztof Prazmowski [10] and by Wojciech Skaba [18]. In this article, we check with the Mizar system [4], some properties on the determinants and the Grassmann-Plücker relation in rank 3 [2], [1], [7],...

Pascal’s Theorem in Real Projective Plane

Roland Coghetto (2017)

Formalized Mathematics

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In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines. For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s...

Combinatorial Grassmannians

Andrzej Owsiejczuk (2007)

Formalized Mathematics

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In the paper I construct the configuration G which is a partial linear space. It consists of k-element subsets of some base set as points and (k + 1)-element subsets as lines. The incidence is given by inclusion. I also introduce automorphisms of partial linear spaces and show that automorphisms of G are generated by permutations of the base set.