Measurable Iso-Functions
American Journal of Modern Physics
Volume 4, Issue 5-1, October 2015, Pages: 24-34
Received: Jun. 2, 2015; Accepted: Jun. 15, 2015; Published: Aug. 11, 2015
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Author
Svetlin G. Georgiev, Department of Mathematics, Sorbonne University, Paris, France
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Abstract
In this article are given definitions definition for measurable is-functions of the first, second, third, fourth and fifth kind. They are given examples when the original function is not measurable and the corresponding iso-function is measurable and the inverse. They are given conditions for the isotopic element under which the corresponding is-functions are measurable. It is introduced a definition for equivalent iso-functions. They are given examples when the iso-functions are equivalent and the corresponding real functions are not equivalent. They are deducted some criterions for measurability of the iso-functions of the first, second, third, fourth and fifth kind. They are investigated for measurability the addition, multiplication of two iso-functions, multiplication of iso-function with an iso-number and the powers of measurable iso-functions. They are given definitions for step iso-functions, iso-step iso-functions, characteristic iso-functions, iso-characteristic iso-functions. It is investigate for measurability the limit function of sequence of measurable iso-functions. As application they are formulated the iso-Lebesgue’s theorems for iso-functions of the first, second, third, fourth and fifth kind. These iso-Lebesgue’s theorems give some information for the structure of the iso-functions of the first, second, third, fourth and fifth kind
Keywords
Measurable Iso-Sets, Measurable Is-Functions, Is-Lebesgue Theorems
To cite this article
Svetlin G. Georgiev, Measurable Iso-Functions, American Journal of Modern Physics. Special Issue: Issue I: Foundations of Hadronic Mathematics. Vol. 4, No. 5-1, 2015, pp. 24-34. doi: 10.11648/j.ajmp.s.2015040501.13
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