Geodesic
Integration of Non-Measurable Functions
Canadian mathematical bulletin, Tome 9 (1966) no. 3, pp. 307-330

Voir la notice de l'article provenant de la source Cambridge University Press

This is primarily an expository paper based on (and generalizing) some ideas of J. Pierpont [6], W.H. Young [8], R. L. Jeffery [4] and S. C. Fan [2]. Our aim is to give a simple and easily applicable theory of integration for arbitrary extended - real functions over arbitrary sets in a measure space. This will be achieved by using a generalized version of Pierpont1 s upper and lower integrals (with the upper integral playing the main role), and by appropriately defining the operations in the extended real number system, henceforth denoted by E*, so as to make it a commutative semigroup under addition and multiplication. 
Zakon, Elias. Integration of Non-Measurable Functions. Canadian mathematical bulletin, Tome 9 (1966) no. 3, pp. 307-330. doi: 10.4153/CMB-1966-040-5
@article{10_4153_CMB_1966_040_5,
     author = {Zakon, Elias},
     title = {Integration of {Non-Measurable} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {307--330},
     year = {1966},
     volume = {9},
     number = {3},
     doi = {10.4153/CMB-1966-040-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-040-5/}
}
TY  - JOUR
AU  - Zakon, Elias
TI  - Integration of Non-Measurable Functions
JO  - Canadian mathematical bulletin
PY  - 1966
SP  - 307
EP  - 330
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-040-5/
DO  - 10.4153/CMB-1966-040-5
ID  - 10_4153_CMB_1966_040_5
ER  - 
%0 Journal Article
%A Zakon, Elias
%T Integration of Non-Measurable Functions
%J Canadian mathematical bulletin
%D 1966
%P 307-330
%V 9
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-040-5/
%R 10.4153/CMB-1966-040-5
%F 10_4153_CMB_1966_040_5

[1] 1. Dieudonné, J., Foundations of Modern Analysis. Academic Press, N.Y., 1960. Google Scholar

[2] 2. Fan, S. C., Integration with respect to an upper measure function, Amer. J. of Mathematics 63 (1941), 319-338. Google Scholar

[3] 3. Halmos, P.R., Measure Theory. D. Van No strand, Princeton 1959. Google Scholar

[4] 4. Jeffery, R. L., Relative summability, Ann. Math. 33 (1932), 443–459. Google Scholar

[5] 5. Munroe, M.E., Intro, to Measure and Integration. Addison- Wesley, 1959. Google Scholar

[6] 6. Pierpont, J., Theory of Functions of Real Var., vol.11, 1912. Google Scholar

[7] 7. Saks, S., Theory of the Integral, Monografie Matematyczne. Warsaw, 1937. Google Scholar

[8] 8. Young, W.H., On the general theory of integration, Philos. Trans. 204(1905), 221-252. Google Scholar

Cité par Sources :