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
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American Journal of Modern Physics (Volume 4, Issue 5-1)
This article belongs to the Special Issue Issue I: Foundations of Hadronic Mathematics |
DOI | 10.11648/j.ajmp.s.2015040501.13 |
Page(s) | 24-34 |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Measurable Iso-Sets, Measurable Is-Functions, Is-Lebesgue Theorems
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APA Style
Svetlin G. Georgiev. (2015). Measurable Iso-Functions. American Journal of Modern Physics, 4(5-1), 24-34. https://doi.org/10.11648/j.ajmp.s.2015040501.13
ACS Style
Svetlin G. Georgiev. Measurable Iso-Functions. Am. J. Mod. Phys. 2015, 4(5-1), 24-34. doi: 10.11648/j.ajmp.s.2015040501.13
AMA Style
Svetlin G. Georgiev. Measurable Iso-Functions. Am J Mod Phys. 2015;4(5-1):24-34. doi: 10.11648/j.ajmp.s.2015040501.13
@article{10.11648/j.ajmp.s.2015040501.13, author = {Svetlin G. Georgiev}, title = {Measurable Iso-Functions}, journal = {American Journal of Modern Physics}, volume = {4}, number = {5-1}, pages = {24-34}, doi = {10.11648/j.ajmp.s.2015040501.13}, url = {https://doi.org/10.11648/j.ajmp.s.2015040501.13}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.s.2015040501.13}, 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}, year = {2015} }
TY - JOUR T1 - Measurable Iso-Functions AU - Svetlin G. Georgiev Y1 - 2015/08/11 PY - 2015 N1 - https://doi.org/10.11648/j.ajmp.s.2015040501.13 DO - 10.11648/j.ajmp.s.2015040501.13 T2 - American Journal of Modern Physics JF - American Journal of Modern Physics JO - American Journal of Modern Physics SP - 24 EP - 34 PB - Science Publishing Group SN - 2326-8891 UR - https://doi.org/10.11648/j.ajmp.s.2015040501.13 AB - 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 VL - 4 IS - 5-1 ER -