This story was originally published on HackerNoon at: https://hackernoon.com/generalized-hausdorff-integral-and-its-applications-basic-notions-and-notations. 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 is available on arxiv(https://arxiv.org/abs/2402.09118) under CC BY-NC-ND 4.0 DEED license. We call f : K → R a simple function, if Ranf is finite. For K ⊂ R, χK will denote the characteristic function of K.