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
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.
S. Georgiev, Foundations of Iso-Dierential Calculus, Vol. 1. Nova Science Publishers, Inc., 2014.
P. Roman and R. M. Santilli, "A Lieadmissible model for dissipative plasma,"Lettere Nuovo Cimento 2, 449-455 (l969).
R. M. Santilli, "Embedding of Lie-algebras into Lie-admissible algebras,"Nuovo Cimento 51, 570 (1967), 33http://www.santillifoundation.org/docs/Santilli-54.pdf
R. M. Santilli, "An introduction to Lieadmissible algebras," Suppl. Nuovo Cimento,6, 1225 (1968).
R. M. Santilli, "Lie-admissible mechanics for irreversible systems." Meccanica, 1, 3 (1969).
R. M. Santilli, "On a possible Lie-admissible covering of Galilei's relativity in Newtonian mechanics for nonconservative and Galilei form-noninvariant systems," . 1, 223-423(1978), available in free pdf download from http://www.santillifoundation.org/docs/Santilli-58.pdf
R. M. Santilli, "Need of subjecting to an Experimental verication the validity within a hadron of Einstein special relativity and Pauli exclusion principle," Hadronic J. 1, 574-901 (1978), available in free pdf download from http://www.santillifoundation.org/docs/Santilli-73.pdf
R. M. Santilli, Lie-admissible Approach to the Hadronic Structure, Vols. I and II, Hadronic Press (1978) http://www.santillifoundation.org/docs/santilli-71.pdf http://www.santillifoundation.org/docs/santilli-72.pdf
R. M. Santilli, Foundation of Theoretical Mechanics, Springer Verlag. Heidelberg, Germany, Volume I (1978), The Inverse Problem in newtonian mechanics, http://www.santillifoundation.org/docs/Santilli-209.pdf Volume II, Birkhoan generalization of hamiltonian mechanics, (1982), http://www.santillifoundation.org/docs/santilli-69.pdf
R. M. Santilli, "A possible Lie-admissibletime-asymmetric model of open nuclear reactions," Lettere Nuovo Cimento 37, 337-344 (1983) http://www.santillifoundation.org/docs/Santilli-53.pdf
R. M. Santilli, "Invariant Lieadmissible formulation of quantum deformations," Found. Phys. 27, 1159- 1177 (1997) http://www.santillifoundation.org/docs/Santilli-06.pdf
R. M. Santilli, "Lie-admissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels," Nuovo Cimento B 121, 443 (2006), http://www.santillifoundation.org/docs//Lie-admiss-NCB-I.pdf
R. M. Santilli and T. Vougiouklis. "Lieadmissible hyperalgebras," Italian Journal of Pure and Applied Mathematics, in press (2013) http://www.santilli-foundation.org/Lie-admhyperstr.pdf
R. M. Santilli, Elements of Hadronic Mechanics, Volumes I and II Ukraine Academy of Sciences, Kiev, second edition 1995, http://www.santillifoundation.org/docs/Santilli-300.pdf http://www.santillifoundation.org/docs/Santilli-301.pdf
R. M. Santilli, Hadronic Mathematics, Mechanics and Chemistry,, Vol. I [18a], II [18b], III [18c], IV [18d] and [18e], International Academioc Press, (2008), available as free downlaods from http://www.i-b-r.org/HadronicMechanics.htm
R. M. Santilli, "Lie-isotopic Lifting of Special Relativity for Extended Deformable Particles," "'Lettere Nuovo Cimento 37, 545 (1983)"', http://www.santillifoundation.org/docs/Santilli-50.pdf
R. M. Santilli, Isotopic Generalizations of Galilei and Einstein Relativities, Volumes Iand II, International Academic Press (1991) , http://www.santillifoundation.org/docs/Santilli-01.pdf 34 http://www.santillifoundation.org/docs/Santilli-61.pdf
R. M. Santilli, "Origin, problematic aspects and invariant formulation of q-, kand other deformations," Intern. J. Modern Phys. 14, 3157 (1999, available as free download from http://www.santillifoundation.org/docs/Santilli-104.pdf
R. M. Santilli, "Isonumbers and Genonumbers of Dimensions 1, 2, 4, 8, their Isoduals and Pseudoduals, and "Hidden Numbers" of Dimension 3, 5, 6, 7," Algebras, Groups and Geometries Vol. 10, 273 (1993), http://www.santillifoundation.org/docs/Santilli-34.pdf
R. M. Santilli, "Nonlocal-Integral Isotopies of Dierential Calculus, Mechanics and Geometries," in Isotopies of Contemporary Mathematical Structures, P. Vetro Editor, Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, 7-82 (1996), http://www.santillifoundation.org/docs/Santilli-37.pdf
R. M. Santilli, "Iso, Geno- Hyper0mathematics for matter and their isoduals for antimatter," Jpournal of Dynamical Systems and Gerometric theories 2, 121-194 (2003)
R. M. Santilli, Acta Applicandae Mathematicae 50, 177 (1998), available as free download from http://www.santillifoundation.org/docs/Santilli-19.pdf
R. M. Santilli, "Isotopies of Lie symmetries," Parts I and II, Hadronic J. 8, 36 - 85(1985), available as free download from http://www.santillifoundation.org/docs/santilli-65.pdf
R. M. Santilli, JINR rapid Comm. 6. 24-38(1993), available as free downlaod from http://www.santillifoundation.org/docs/Santilli-19.pdf
R. M. Santilli, "Apparent consistency of Rutherford's hypothesis on the neutron as a compressed hydrogen atom, Hadronic J. 13, 513 (1990). http://www.santillifoundation.org/docs/Santilli-21.pdf
R. M. Santilli, "Apparent consistency of Rutherford's hypothesis on the neutron structure via the hadronic generalization of quantum mechanics - I: Nonrelativistic treatment", ICTP communication IC/91/47 (1992) http://www.santillifoundation.org/docs/Santilli-150.pdf
R. M. Santilli, "Recent theoretical and experimental evidence on the apparent synthesis of neutrons from protons and electrons.", Communication of the Joint Institute for Nuclear Research, Dubna, Russia, number JINR-E4-93-352 (1993)
R.M. Santilli, "Recent theoretical and experimental evidence on the apparent synthesis of neutrons from protons and electrons," Chinese J. System Engineering and Electronics Vol. 6, 177-199 (1995) http://www.santillifoundation.org/docs/Santilli-18.pdf
Santilli, R. M. Isodual Theory of Antimatter with Applications to Antigravity, Grand Unication and Cosmology, Springer(2006).
R. M. Santilli, "A new cosmological conception of the universe based on the isominkowskian geometry and its isodual," Part I pages 539-612 and Part II pages, Contributed paper in Analysis, Geometry and Groups, A Riemann Legacy Volume, Volume II, pp. 539-612 H.M. Srivastava, Editor, International Academic Press (1993)
R. M. Santilli, "Representation of antiparticles via isodual numbers, spaces and geometries," Comm. Theor. Phys. 1994 3, 153-181 http://www.santillifoundation.org/docs/Santilli-112.pdfAntigravity
R. M. Santilli, "Antigravity," Hadronic J. 1994 17, 257-284 http://www.santillifoundation.org/docs/Santilli-113.pdfAntigravity
R. M. Santilli, "Isotopic relativity for matter and its isodual for antimatter," Gravitation 1997, 3, 2.
R. M. Santilli, "Isominkowskian Geometry for the Gravitational Treatment of Matter and its Isodual for Antimatter," Intern. J. Modern Phys. 1998, D 7, 351 http://www.santillifoundation.org/docs/Santilli-35.pdfR.
R. M. Santilli, "Lie-admissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels," Nuovo Cimento B, Vol. 121, 443 (2006) http://www.santillifoundation.org/docs/Lie-admiss-NCB-I.pd
R. M. Santilli, "The Mystery of Detecting Antimatter Asteroids, Stars and Galaxies," American Institute of Physics, Proceed. 2012, 1479, 1028-1032 (2012) http://www.santillifoundation.org/docs/antimatterasteroids.pdf.