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We use nonstandard techniques, in the sense of Abraham Robinson, to give the exact Hausdorff outer measure.
Dimension und äußeres Maß
Felix Hausdorff · 1918
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Modern theories of integration
Hyman Kestelman · 1960
Earlier work this paper cites.
Geometric measure theory
Herbert Federer · 1969
Earlier work this paper cites.
Hausdorff measures
Claude A. Rogers · 1970
Earlier work this paper cites.
A model of set-theory in which every set of reals is Lebesgue measurable
Robert M. Solovay · 1970
Earlier work this paper cites.
Non-standard analysis
Abraham Robinson · 1974
Earlier work this paper cites.
Nonstandard methods in stochastic analysis and mathematical physics
Sergio Albeverio, Raphael Høegh-Krohn, Jens Erik Fenstad, and Tom Lindstrøm · 1986
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Unsolved problems in geometry
Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy · 1991
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On the equality of Hausdorff and box counting dimensions
Ronnie Mainieri · 1993
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Nonstandard real analysis
Nigel J. Cutland · 1997
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Measure theory. Vol. 1
David H. Fremlin · 2000
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Measure theory. Vol. 2
David H. Fremlin · 2001
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Measure theory. Vol. 3
David H. Fremlin · 2002
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Chaos in dynamical systems
Edward Ott · 2002
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Measure theory. Vol. 4
David H. Fremlin · 2003
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Nonstandard analysis
Alain M. Robert · 2003
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Maß- und Integrationstheorie
Jürgen Elstrodt · 2005
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Measure theory. Vol. 5. Set-theoretic measure theory. Part II
David H. Fremlin · 2008
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Accuracy Analysis of the Box-Counting Algorithm
Andrzej Górski, Stanisław Drożdż, Agnieszka Mokrzycka, and Jakub Pawlik · 2012
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