Boolean Valued Analysis

Kusraev, A. G.; Kutateladze, S. S.

doi:10.1007/978-94-011-4443-8

Cited by 76 publications

(138 citation statements)

References 19 publications

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“…We continue with further basic notions in LNOVSs, which are motivated by their analogies for vector lattices and for LNVLs (see, for example, [4][5][6]19,20,[25][26][27]). …”

Section: Proposition 1 Let the Positive Conementioning

confidence: 99%

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Nonstandard hulls of lattice-normed ordered vector spaces

Aydın¹,

Gorokhova²,

Gül³

2018

Turk J Math

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Nonstandard hulls of a vector lattice were introduced and studied in many papers. Recently, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space due to Emelyanov, we describe and investigate the nonstandard hull of a lattice-normed space, which is the foregoing generalization of Luxemburg's nonstandard hull of a normed space.

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“…We continue with further basic notions in LNOVSs, which are motivated by their analogies for vector lattices and for LNVLs (see, for example, [4][5][6]19,20,[25][26][27]). …”

Section: Proposition 1 Let the Positive Conementioning

confidence: 99%

“…Note that a vector lattice E can be seen as the corresponding LNS (E, | · |, E). Lattice-normed vector lattices (abbreviated by LNVLs) have attracted attention in [4,5,10,12,14,26,27]. The general theory of lattice-normed ordered vector spaces (abbreviated by LNOVSs) is still under investigation.…”

Section: Introductionmentioning

confidence: 99%

Nonstandard hulls of lattice-normed ordered vector spaces

Aydın¹,

Gorokhova²,

Gül³

2018

Turk J Math

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“…[8]). The modern technique of mathematical modeling opened an opportunity to demonstrate that the principal properties of lattice normed spaces represent the Boolean valued interpretations of the relevant properties of classical normed spaces.…”

Section: Functional Analysis and Applied Mathematicsmentioning

confidence: 99%

“…The function then of analysis and deduction in economics is not to forge a few long chains of reasoning, but to forge rightly many short chains and single connecting links... 8 It is obvious that there is no room in economics for long trains of deductive reasoning. 9 In 1906 Marshall formulated his scepticism in regard to mathematics as follows:…”

Section: Consolidation Of Mindmentioning

confidence: 99%

Mathematics and economics of Leonid Kantorovich

Kutateladze

2012

Sib Math J

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“…The other consists in applying the standard monadology inside the Boolean valued universe V (B) over a complete Boolean algebra B, while ascending and descending by the Escher rules (cp. [1] and [2]). …”

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Leibnizian, Robinsonian, and Boolean valued monads

Kutateladze

2011

J. Appl. Ind. Math.

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Abstract-This is an overview of the present-day versions of monadology with some applications to vector lattices and linear inequalities. Two approaches to combining nonstandard set-theoretic models are sketched and illustrated by order convergence, principal projection, and polyhedrality. DOI: 10.1134/S1990478911030082Keywords: Dedekind complete vector lattice, filter, fragments, principal projection, order convergence, up-down, descent, ascent, polyhedral Lagrange principle, Boolean valued model The notion of monad is central to external set theory. Justifying the simultaneous use of infinitesimals and the technique of descending and ascending in vector lattice theory requires adaptation of monadology for the implementation of filters in Boolean valued universes. This is still a rather uncharted area of research. The two approaches are available now. One is to apply monadology to the descents of objects. The other consists in applying the standard monadology inside the Boolean valued universe V (B) over a complete Boolean algebra B, while ascending and descending by the Escher rules (cp.[1] and [2]).These approaches are sketched and illustrated by tests for order convergence and rules for fragmenting and projecting positive operators in vector lattices. Also, Lagrange's principle is shortly addressed in polyhedral environment with inexact data.

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Boolean Valued Analysis

Cited by 76 publications

References 19 publications

Nonstandard hulls of lattice-normed ordered vector spaces

Nonstandard hulls of lattice-normed ordered vector spaces

Mathematics and economics of Leonid Kantorovich

Leibnizian, Robinsonian, and Boolean valued monads

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