Generalized Hausdorff Integral and Its Applications: References

Author: (1) Attila Losonczi. Table of Links Abstract and 1 Introduction 1.1 Basic notions and notations 1.2 Basic definitions from [7] and [8] 2 Generalized integral 2.1 Multiplication on [0, +∞) × [−∞, +∞] 2.2 Measurability 2.3 The integral of functions taking values in [0, +∞) × [0, +∞) 3 Applications 4 References 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 This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Author: (1) Attila Losonczi. Author: Author: (1) Attila Losonczi. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Basic notions and notations 1.1 Basic notions and notations 1.2 Basic definitions from [7] and [8] 1.2 Basic definitions from [7] and [8] 2 Generalized integral 2.1 Multiplication on [0, +∞) × [−∞, +∞] 2.1 Multiplication on [0, +∞) × [−∞, +∞] 2.2 Measurability 2.2 Measurability 2.3 The integral of functions taking values in [0, +∞) × [0, +∞) 2.3 The integral of functions taking values in [0, +∞) × [0, +∞) 3 Applications 3 Applications 4 References 4 References 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 This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv