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Showing 1 to 12 of 12 for “"nonstandard analysis"”.
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Nonstandard analysis based calculus
… half of this project develops the basics of Nonstandard Analysis, including the theory of ultrafilters, and the formal construction of the Hyperreals.
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Nonstandard analysis based calculus
… half of this project develops the basics of Nonstandard Analysis, including the theory of ultrafilters, and the formal construction of the Hyperreals.
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Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis
… be called Mac Lane’s thesis—the thesis that nonstandard analysis (NSA) and smooth infinitesimal analysis (SIA) are alternatives to the standard approach to the calculus. In doing so, we outline the historical approaches to the calculus, the standard approach to the calculus, and two …
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Hyperreal structures arising from an infinite base logarithm
… of infinite and infinitesimal numbers in real analysis. theory is based upon the hyperreal number system developed by Abraham Robinson in the 1960's in his invention of "nonstandard analysis". paper begins with a short exposition of the construction of the hyperreal nU1l1ber system and the …
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Convergence in incomplete market models
… in incomplete market models.Techniques from nonstandard analysis are used to develop new results for the lifting property of the minimal martingale density and risk-minimising strategies. These are applied to a number of incomplete market models:The restriction of hedging dates in a general …
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Tripos models of Internal Set Theory
… of E. Nelson’s Internal Set Theory (and hence of nonstandard analysis) in elementary toposes by exploiting the technology of tripos theory and Lawvere’s hyperdoctrines. A new doctrinal account of nonstandard phenomena is described, which avoids a few key restrictions in Nelson’s approach: chiefly, …
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Internal Set Theory and Euler's Introductio in Analysin Infinitorum
… techniques from Abraham Robinson's celebrated Nonstandard Analysis (NSA); in particular, we will use Internal Set Theory, Edward Nelson's distinctive version of NSA. We will specifically examine Euler's proofs of the Euler formula, the Euler product, the Wallis product and the divergence of the …
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Nonstandard vector integrals and vector measures
… can be approximated by simple functions. Using Nonstandard Analysis, we investigate internal simple functions from an internal measure space to the nonstandard extension of a Banach space. We take suitable equivalence classes and identify the subspace of S-integrable functions with a space of …
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Nonstandard Methods in Lie Theory
… These applications of model theory come via nonstandard analysis. In Lie theory, we use nonstandard methods to prove two results. First, we give a positive solution to the local form of Hilbert's Fifth Problem, which asks whether every locally euclidean local topological group is locally …
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Nonstandard Models in Measure Theory and in functional Analysis
This thesis is concerned with the study of nonstandard models in measure theory and in functional analysis. In measure theory, we define elementary numerosities, that are additive measures that take on values in a non-archimedean field and for which the measure of every singleton is 1. We have …
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Nonstandard techniques in lifting theory
In this dissertation, a nonstandard approach to lifting theory developed by Bliedtner and Loeb is applied to liftings on topological measure spaces and group measure spaces. A further application to disintegrations of measures is given.
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Neuroeconomics of Reward Information and Motivation
… in models.</p><p>Chapters 3 and 4 employ a nonstandard analysis technique, multivariate pattern analysis (MVPA), to identify brain regions that contain information associated with different types of economic valuation. Chapter 3 uses a combinatoric approach to evaluate how brain regions …