Neutrosophic Non-Newtonian and Geometric Measures: A  Consistent Analytical Framework

Amer Darweesh; Kamel Al-Khaled; Mohammed Shakhatreh; Mahmood Shareef Ajeel; Nermin Abo  Hasan

Authors

Amer Darweesh Department of Mathematics and Stat., Jordan University of Science and Technology, Irbid 22110, Jordan;
Kamel Al-Khaled Department of Mathematics and Stat., Jordan University of Science and Technology, Irbid 22110, Jordan;
Mohammed Shakhatreh Department of Mathematics and Stat., Jordan University of Science and Technology, Irbid 22110, Jordan;
Mahmood Shareef Ajeel Department of Material Engineering- College of Engineering, Shatrah University, Thi-Qar 64001- Iraq
Nermin Abo Hasan Department of Mathematics and Stat., Jordan University of Science and Technology, Irbid 22110, Jordan;

Keywords:

Geometric calculus, Geometric measure, Neutrosophic measure, Geometric outer measure, Geometric Lebesgue measure.

Abstract

The neutrosophic measure is a generalization of the classical measure in situations when the space
contains some indeterminacy. In this paper, we introduce the concept of the Neutrosophic Geometric Measure,
we also provide some results, and examples related to the Neutrosophic Geometric Measure. A classical measure
of the objects determinate component, a classical measure of its indeterminate part, and a further classical
measure of the objects opposite determinate part are the three classical measures that make up the neutrosophic
measure. To de ne the Neutrosophic Geometric Measure, we introduce a new measure on R+ and call it
the geometric Lebesgue measure. The geometric Lebesgue measure is de ned, and some of its properties
are examined and detailed. Moreover, we establish a relation between the Lebesgue measure and geometric
Lebesgue measure to see if the properties of Lebesgue measure are still true in this new measure. Other
basic topics discussed in this paper are geometric measurable function and the geometric simple approximation
Theorem

DOI: 10.5281/zenodo.14708738