In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesque quadratic stochastic operator on the set of all Lebesque measures of the set [0,1] and prove the regularity of the Lebesque quadratic stochastic operators.
REFERENCES
1.
2.
H.
Kesten
, Adv. App. Prob.
2
, 1
–82
(1970
).3.
Yu.
Lyubich
, Mathematical Structures in Population Genetics
(Springer-Verlag
, Berlin
, 1992
).4.
5.
N.
Ganikhodjaev
, R.
Ganikhodjaev
and U.
Jamilov
, Ergodic Theory and Dynamical Systems
35
(5
), 1443
–1473
(2015
).6.
N.
Ganikhodjaev
, M.
Saburov
and U.
Jamilov
App Math Info Sci
7
, 1721
–1729
(2013
).7.
8.
N.
Ganikhodjaev
and D.
Zanin
, Russian Math. Surveys
59
(3
), 571
–572
(2004
).9.
M.
Zakharevich
, Russian Math.Surveys
33
(6
), 265
–266
(1978
).10.
R.
Ganikhodzhaev
, F.
Mukhamedov
and U.
Rozikov
, Infinite Dimensional Analysis, Quantum Probability and Related Topics
14
(2
), 279
–335
(2011
).11.
12.
R.
Ganikhodzhaev
, Math. Notes
56
(5-6
), 1125
–1131
(1994
).13.
R.
Ganikhodzhaev
, Acad. Sci. Sb.Math.
76
(2
), 489
–506
(1993
).
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