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Author:
(1) Attila Losonczi.
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Table of Links
1.1 Basic notions and notations
1.2 Basic definitions from [7] and [8]
2 Generalized integral
2.1 Multiplication on [0, +∞) × [−∞, +∞]
2.3 The integral of functions taking values in [0, +∞) × [0, +∞)
4 References
[1] Billingsley, P., Probability and Measure, John Wiley & Sons, vol. 939 (2012).
[2] Bruckner, A. M.; Bruckner, J. B.; Thomson, B. S., Real Analysis, CreateSpace Independent Publishing Platform; 2nd edition (July 31, 2008)
[3] Engelking, R., Dimension theory, North-Holland Publishing Company (1978).
[4] Falconer, Kenneth, Fractal geometry: mathematical foundations and applications, John Wiley & Sons (2004).
[5] Kurtz, Douglas S.; Swartz, Charles W., Series in Real Analysis, Theories of integration: The Integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, World Scientific Publishing Company (2011).
[6] Losonczi, Attila, Dimension structures, Journal of Classical Analysis 14, Number 1 (2019), 69–95.
[7] Losonczi, Attila, The Hausdorff-integral and its applications, arXiv preprint, http://arxiv.org/abs/2401.11465.
[8] Losonczi, Attila, The Hausdorff-integral on h-measure spaces, arXiv preprint, https://arxiv.org/abs/2402.09118v2.
[9] Losonczi, Attila, Measuring the deficiency of properties in analysis, topology and geometry, (2023), in preparation
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This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license.
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