Geodesic
Finite probabilistic structures
Diskretnaya Matematika, Tome 20 (2008) no. 3, pp. 19-27.

Voir la notice de l'article provenant de la source Math-Net.Ru

Consideration of the field of events in the theory of probability gives rise to the notion of the field of events $\mathscr F(B)$ consisting of a set of subsets of some set $B$. On the field $\mathscr F(B)$, two algebraic structures are naturally defined. These are the Boolean algebra $\mathscr A(\mathscr F(B))$ with the operations of union, intersection and complement, and the lattice $L(\mathscr F(B))$, where the order is defined according to inclusion of the sets of $\mathscr F(B)$. In this paper, we consider one more algebraic structure on $\mathscr F(B)$ and the abstract variant of this structure, the so-called probabilistic structure, which is closely related to properties of the measure on $\mathscr F(B)$. 
@article{DM_2008_20_3_a1,
     author = {V. M. Maksimov},
     title = {Finite probabilistic structures},
     journal = {Diskretnaya Matematika},
     pages = {19--27},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2008_20_3_a1/}
}
TY  - JOUR
AU  - V. M. Maksimov
TI  - Finite probabilistic structures
JO  - Diskretnaya Matematika
PY  - 2008
SP  - 19
EP  - 27
VL  - 20
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2008_20_3_a1/
LA  - ru
ID  - DM_2008_20_3_a1
ER  - 
%0 Journal Article
%A V. M. Maksimov
%T Finite probabilistic structures
%J Diskretnaya Matematika
%D 2008
%P 19-27
%V 20
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2008_20_3_a1/
%G ru
%F DM_2008_20_3_a1
V. M. Maksimov. Finite probabilistic structures. Diskretnaya Matematika, Tome 20 (2008) no. 3, pp. 19-27. http://geodesic.mathdoc.fr/item/DM_2008_20_3_a1/

[1] Sikorskii R., Bulevy algebry, Mir, Moskva, 1969 | MR

[2] Birkgof G., Teoriya reshetok, Nauka, Moskva, 1984 | MR

[3] Maksimov V. M., “Veroyatnostnye struktury i veroyatnostnye mnozhestva”, Uspekhi matem. nauk, 62:6(378) (2007), 181–182 | MR | Zbl

[4] Dirac P. A. M., “On the analogy between classical and quantum mechanics”, Rev. Modern Phys., 17 (1945), 195–199 | DOI | MR | Zbl

[5] Feynman R. P., “Negative probability”, Quantum implications, Routledge and Kegan Paul, London, 1987, 235–248 | MR

[6] Khrennikov A. Yu., “$p$-adicheskaya veroyatnost i statistika”, Dokl. RAN, 322 (1992), 1075–1079 | MR | Zbl

[7] Khrennikov A. Yu., $p$-adic valued distributions and their applications to the mathematical physics, Kluwer, Dordrecht, 1994 | Zbl

[8] Khrennikov A. Yu., “O rasshirenii chastotnogo podkhoda R. fon Mizesa i aksiomaticheskogo podkhoda A. N. Kolmogorova na $p$-adicheskuyu teoriyu veroyatnostei”, Teoriya veroyatnostei i ee primeneniya, 40:2 (1995), 458–464 | MR | Zbl

[9] Khrennikov A. Yu., Nearkhimedov analiz i ego primeneniya, Nauka, Moskva, 2003

[10] Khrennikov A. Yu., “Generalized probabilities taking values in non-Archimedean fields and topological groups”, Russ. J. Math. Phys., 14:2 (2007), 142–159 | DOI | MR | Zbl

[11] Vladimirov V. S., Volovich I. V., Zelenov E. I., $p$-adic analysis and mathematical physics, World Scientific, Singapore, 1994 | MR | Zbl

[12] Khrennikov A. Yu., “$p$-adic quantum mechanics with $p$-adic valued functions”, J. Math. Phys., 32:4 (1991), 932–937 | DOI | MR | Zbl

[13] Khrennikov A. Yu., “Teorema Bernulli dlya veroyatnostei, prinimayuschikh $p$-adicheskie znacheniya”, Dokl. RAN, 354:4 (1997), 461–464 | MR

[14] Maximov V. M., “Abstract models of probabilities”, Foundations of probability and physics, QP–PQ: Quantum Probab. White Noise Anal., 13, World Scientific, River Edge, 2007, 257–273 | MR

[15] Maximov V. M., “The set of abstract probabilities”, Foundations of Probability and Physics, ATP Conf. Proc., Amer. Inst. Phys., Melville, 2007, 353–361