Approximations of Nonlinear Integral Functionals of Entropy Type
Informatics and Automation, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 7-18 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtain generalizations and strengthenings of the results of V. V. Kozlov and D. V. Treschev on approximations of nonlinear integral functionals of entropy type on measure spaces.
Keywords: integral functional, entropy, conditional expectation.
@article{TRSPY_2020_310_a0,
     author = {V. I. Bogachev},
     title = {Approximations of {Nonlinear} {Integral} {Functionals} of {Entropy} {Type}},
     journal = {Informatics and Automation},
     pages = {7--18},
     year = {2020},
     volume = {310},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2020_310_a0/}
}
TY  - JOUR
AU  - V. I. Bogachev
TI  - Approximations of Nonlinear Integral Functionals of Entropy Type
JO  - Informatics and Automation
PY  - 2020
SP  - 7
EP  - 18
VL  - 310
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2020_310_a0/
LA  - ru
ID  - TRSPY_2020_310_a0
ER  - 
%0 Journal Article
%A V. I. Bogachev
%T Approximations of Nonlinear Integral Functionals of Entropy Type
%J Informatics and Automation
%D 2020
%P 7-18
%V 310
%U http://geodesic.mathdoc.fr/item/TRSPY_2020_310_a0/
%G ru
%F TRSPY_2020_310_a0
V. I. Bogachev. Approximations of Nonlinear Integral Functionals of Entropy Type. Informatics and Automation, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 7-18. http://geodesic.mathdoc.fr/item/TRSPY_2020_310_a0/

[1] Bogachev V.I., Measure theory, v. 1, 2, Springer, New York, 2007 | MR | Zbl

[2] Bogachev V.I., Weak convergence of measures, Math. Surv. Monogr., 234, Amer. Math. Soc., Providence, RI, 2018 | DOI | MR | Zbl

[3] V. I. Bogachev, “Non-uniform Kozlov–Treschev averagings in the ergodic theorem”, Russ. Math. Surv., 75:3 (2020), 393–425 | DOI | MR | Zbl

[4] V. I. Bogachev and A. A. Lipchyus, “Approximation of nonlinear integral functionals”, Dokl. Math., 80:2 (2009), 749–754 | DOI | MR | MR | Zbl

[5] Bogachev V.I., Smolyanov O.G., Real and functional analysis, Moscow Lect., 4, Springer, Cham, 2020 | DOI | Zbl

[6] Braides A., Defranceschi A., Homogenization of multiple integrals, Oxford Lect. Ser. Math. Appl., 12, Clarendon Press, Oxford, 1998 | MR | Zbl

[7] Giaquinta M., Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. Math. Stud., 105, Princeton Univ. Press, Princeton, 1983 | MR | Zbl

[8] Giaquinta M., Hildebrandt S., Calculus of variations, v. I, Grundl. Math. Wiss., 310, The Lagrangian formalism, Springer, Berlin, 1996 | MR | Zbl

[9] Giaquinta M., Hildebrandt S., Calculus of variations. II: The Hamiltonian formalism, Grundl. Math. Wiss., 311, Springer, Berlin, 1996 | MR

[10] V. V. Kozlov, “The generalized Vlasov kinetic equation”, Russ. Math. Surv., 63:4 (2008), 691–726 | DOI | MR | Zbl

[11] Kozlov V.V., “Coarsening in ergodic theory”, Russ. J. Math. Phys., 22:2 (2015), 184–187 | DOI | MR | Zbl

[12] V. V. Kozlov and D. V. Treshchev, “Fine-grained and coarse-grained entropy in problems of statistical mechanics”, Theor. Math. Phys., 151:1 (2007), 539–555 | DOI | MR | Zbl

[13] M. A. Krasnosel'ski{ĭ} and Ya. B. Ruticki{ĭ}, Convex Functions and Orlicz Spaces, Fizmatgiz, Moscow, 1958 | MR | Zbl

[14] Noordhoff, Groningen, 1961 | MR | Zbl

[15] M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions, Nauka, Moscow, 1966 | MR | Zbl | Zbl

[16] Noordhoff, Leiden, 1976 | MR | Zbl | Zbl

[17] V. L. Levin, Convex Analysis in Spaces of Measurable Functions and Its Application in Mathematics and Economics, Nauka, Moscow, 1985 (in Russian) | MR | Zbl

[18] Piftankin G., Treschev D., “Coarse-grained entropy in dynamical systems”, Regul. Chaotic Dyn., 15:4–5 (2010), 575–597 | DOI | MR | Zbl

[19] Rao M.M., Ren Z.D., Theory of Orlicz spaces, Pure Appl. Math., 146, M. Dekker, New York, 1991 | MR | Zbl

[20] Väth M., “A general theorem on continuity and compactness of the Uryson operator”, J. Integral Eqns. Appl., 8:3 (1996), 379–389 | DOI | MR | Zbl

[21] Väth M., “Approximation, complete continuity, and uniform measurability of Uryson operators on general measure spaces”, Nonlinear Anal. Theory Methods Appl., 33:7 (1998), 715–728 | DOI | MR | Zbl