On Recursive Decompositions of Measures
Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 720-729.

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

Recursive decompositions of a complex measure relative to a nonnegative measure are considered and properties of the decompositions and conditions for convergence are established.
Keywords: recursive decomposition of a complex measure, convergence of a recursive series, Radon–Nikodym theorem, absolutely continuous measure.
Mots-clés : Lebesgue measure
@article{MZM_2012_91_5_a7,
     author = {T. P. Lukashenko},
     title = {On {Recursive} {Decompositions} of {Measures}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {720--729},
     publisher = {mathdoc},
     volume = {91},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a7/}
}
TY  - JOUR
AU  - T. P. Lukashenko
TI  - On Recursive Decompositions of Measures
JO  - Matematičeskie zametki
PY  - 2012
SP  - 720
EP  - 729
VL  - 91
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a7/
LA  - ru
ID  - MZM_2012_91_5_a7
ER  - 
%0 Journal Article
%A T. P. Lukashenko
%T On Recursive Decompositions of Measures
%J Matematičeskie zametki
%D 2012
%P 720-729
%V 91
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a7/
%G ru
%F MZM_2012_91_5_a7
T. P. Lukashenko. On Recursive Decompositions of Measures. Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 720-729. http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a7/

[1] N. Danford, Dzh. Shvarts, Lineinye operatory. T. 1. Obschaya teoriya, IL, M., 1962 | MR | Zbl

[2] V. I. Bogachev, O. G. Smolyanov, Deistvitelnyi i funktsionalnyi analiz: universitetskii kurs, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.–Izhevsk, 2009

[3] T. P. Lukashenko, V. A. Sadovnichii, “O rekursivnykh razlozheniyakh po tsepochke sistem”, Dokl. RAN, 425:6 (2009), 741–746 | MR | Zbl

[4] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 2004 | MR | Zbl

[5] T. P. Lukashenko, “O rekursivnykh razlozheniyakh funktsii i mer”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Materialy 15-i Saratovskoi zimnei shkoly, posvyaschennoi 125-letiyu so dnya rozhdeniya V. V. Golubeva i 100-letiyu SGU, Izd-vo Saratovsk. un-ta, Saratov, 2010, 102–105

[6] T. P. Lukashenko, “O rekursivnykh razlozheniyakh mer”, Sovremennye problemy analiza i prepodavaniya matematiki, Materialy mezhdunarodnoi nauchoi konferentsii, posvyaschennoi 105-letiyu akadademika S. M. Nikolskogo, Izd-vo TsPI pri mekh.-matem. f-te MGU, M., 2010, 27

[7] T. P. Lukashenko, “Rekursivnye razlozheniya mer”, XVIII mezhdunarodnaya konferentsiya “Matematika. Ekonomika. Obrazovanie”, VI mezhdunarodnyi simpozium “Ryady Fure i ikh prilozheniya”. Mezhdistsiplinarnyi seminar “Informatsionno-kommunikatsionnye tekhnologii”, Tezisy dokladov, Izd-vo SKNTs VSh YuFU, Rostov-na-Donu, 2010, 19

[8] T. P. Lukashenko, “Rekursivnye razlozheniya mer”, Mezhdunarodnaya konferentsiya “Metricheskaya geometriya poverkhnostei i mnogogrannikov”, posvyaschennaya 100-letiyu so dnya rozhdeniya Nikolaya Vladimirovicha Efimova, Sbornik tezisov, MAKS Press, M., 2010, 89