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A nonstandard proof of a lemma from constructive measure theory
Mathematical Logic Quarterly, 2006AbstractSuppose that fn is a sequence of nonnegative functions with compact support on a locally compact metric space, that T is a nonnegative linear functional, and that $ \sum ^\infty _{n=1}$ T fn < T f0. A result of Bishop, foundational to a constructive theory of functional analysis, asserts the existence of a point x such that $ \sum ^\infty _ ...
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Counterexamples in Nonstandard Measure Theory
Canadian Mathematical Bulletin, 1995AbstractWe 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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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
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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
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Recent developments in problems with nonstandard growth and nonuniform ellipticity
Journal of Mathematical Analysis and Applications, 2021Giuseppe Mingione +1 more
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Time to add screening for financial hardship as a quality measure?
Ca-A Cancer Journal for Clinicians, 2021Cathy J Bradley +2 more
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