Results 1 to 10 of about 30,830 (118)
Nonstandard Methods in Measure Theory [PDF]
Abstract and Applied Analysis, 2014 Ideas and techniques from standard and nonstandard theories of measure spaces and Banach spaces are brought together to give a new approach to the study of the extension of vector measures.
Grigore Ciurea
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Lifting Theorems in Nonstandard Measure Theory [PDF]
Proceedings of the American Mathematical Society, 1990 1. A nonstandard capacity construction, analogous to Loeb’s measure construction, is developed. Using this construction and Choquet’s Capacitability theorem, it is proved that a Loeb measurable function into a general (not necessarily second countable) space has a lifting precisely when its graph is ’almost’ analytic.
David A. Ross
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Nonstandard Measure Theory-Hausdorff Measure [PDF]
Proceedings of the American Mathematical Society, 1977 In this paper it is shown that the Hausdorff measures λ t {\lambda ^t} for t ∈ [ 0 , ∞ ) t \in [0,\infty ) can be simultaneously represented as ∗ ^\ast finite counting measures in an appropriate ...
Frank Wattenberg
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CONSTRUCTING NONSTANDARD HULLS AND LOEB MEASURES IN INTERNAL SET THEORIES [PDF]
The Bulletin of Symbolic Logic, 2022 AbstractCurrently the two popular ways to practice Robinson’s nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the internal axiomatic approach is unable to handle constructions relying on external sets.
KAREL HRBACEK, MIKHAIL G. KATZ
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Conversion from nonstandard to standard measure spaces and applications in probability theory [PDF]
Transactions of the American Mathematical Society, 1975 Let ( X , A , ν ) (X,\mathcal {A},\nu ) be an internal measure space in a denumerably comprehensive enlargement. The set X is a standard measure space when equipped with the smallest standard σ \sigma -algebra M \mathfrak {M}
Peter A. Loeb
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Nonstandard Measure Theory: Avoiding Pathological Sets [PDF]
Transactions of the American Mathematical Society, 1979 The main results in this paper concern representing Lebesgue measure by nonstandard measures which avoid certain pathological sets. An (external) set E is S-thin if InfmA|A standard,* A ⊇ E A\, \supseteq \,E = 0 and Q-thin if Inf*mA|A internal, A ⊇ E
Frank Wattenberg
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Counterexamples in Nonstandard Measure Theory [PDF]
Canadian Mathematical Bulletin, 1995 AbstractWe show that several "good" properties of the standard part map on regular Hausdorff spaces do not hold for arbitrary Hausdorff spaces.
Aldaz, J. M., Loeb, P. A.
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Nonstandard approach to Hausdorff measure theory and an analysis of some sets of dimension less than $1$ [PDF]
, 2018 103 pages. This was the author's Master of Philosophy thesis. Theorem 5.2.2.
Mee Seong Im
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Nonstandard Approach to Hausdorff Measure Theory and An Analysis of Some Sets of Dimension Less Than 1 [PDF]
, 2004 We study various measure theories using the classical approach and then compute the Hausdorff dimension of some simple objects and self-similar fractals. We then develop a nonstandard approach to these measure theories and examine the Hausdorff measure in more detail. We choose to study Hausdorff measure over any other measures since it is well-defined
Mee Seong Im
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Nonstandard Models in Measure Theory and in functional Analysis
, 2017 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.
Emanuele Bottazzi
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