Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part X, Tome 107 (1982), pp. 136-149
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A. A. Mekler. The countable partition averaging operator with respect to a minimal rearrangement invariant ideal of the space $L^1(0,1)$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part X, Tome 107 (1982), pp. 136-149. http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a7/
@article{ZNSL_1982_107_a7,
author = {A. A. Mekler},
title = {The countable partition averaging operator with respect to a~minimal rearrangement invariant ideal of the space $L^1(0,1)$},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {136--149},
year = {1982},
volume = {107},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a7/}
}
TY - JOUR
AU - A. A. Mekler
TI - The countable partition averaging operator with respect to a minimal rearrangement invariant ideal of the space $L^1(0,1)$
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1982
SP - 136
EP - 149
VL - 107
UR - http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a7/
LA - ru
ID - ZNSL_1982_107_a7
ER -
%0 Journal Article
%A A. A. Mekler
%T The countable partition averaging operator with respect to a minimal rearrangement invariant ideal of the space $L^1(0,1)$
%J Zapiski Nauchnykh Seminarov POMI
%D 1982
%P 136-149
%V 107
%U http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a7/
%G ru
%F ZNSL_1982_107_a7
In terms of functions $f^*$ and $f^{**}$ the necessary and sufficient conditions are given for the validity of the inclusion $\mathsf E(N_f|\mathscr T)\subset N_f$ where $f$ is an arbitrary element of $L^1(0,1)$, $N_f$, $f$, $\mathscr T$ is the minimal rearrangement invariant ideal of $L^1(0,1)$ containing $f$, $\mathscr T$ is a partition of the segment [0,1] by points of a sequence $t_n\downarrow0$ and $\mathsf E(\cdot|\mathscr T)$ is the conditional expectation operator.
