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by HausdorffJuly 18th, 2024

**Author:**

(1) Attila Losonczi.

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, +∞)

[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

This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license.

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