This story was originally published on HackerNoon at: https://hackernoon.com/generalized-hausdorff-integral-and-its-applications-abstract-and-introduction. Exploring a generalized Hausdorff integral for functions in [0, +∞) × [0, +∞), extending from earlier work on h-measure spaces and dimensionality. Check more stories related to tech-stories at: https://hackernoon.com/c/tech-stories. You can also check exclusive content about #hausdorff-integral, #generalized-integral, #h-measure-spaces, #dimension-theory, #measurable-functions, #mathematical-analysis, #function-integration, #applied-mathematics, and more. This story was written by: @hausdorff. Learn more about this writer by checking @hausdorff's about page, and for more stories, please visit hackernoon.com. This paper can be considered as a continuation of the papers 7 and 8. In all our intentions, we follow the same attitude that we had in our previous investigations, i.e. we work in the realm of Hausdorff dimension and measure. The new integral has the usual properties, e.g. it is a linear functional, monotone, it provides an h-measure, etc.