Caratheodory dimension for observers

Document Type : Research Paper


Department of Pure Mathematics‎, ‎Faculty of Mathematics and Computer‎, ‎Shahid Bahonar University of Kerman‎, ‎Kerman‎, ‎Iran.


‎In this essay we introduce and study the notion of dimension for observers via Caratheodory structures and relative probability measures‎. ‎We show that the dimension as a three variables function is an increasing function on observers‎, ‎and decreasing function on the cuts of an observer‎. ‎We find observers with arbitrary non-negative dimensions‎. ‎We show that Caratheodory dimension for observers is an invariant object under conjugate relations‎. ‎Caratheodory dimension as a mapping‎, ‎for multi-dimensional observers is considered‎. ‎News spread is modeled via multi-dimensional observers‎.


Main Subjects

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