Geodesic
Extension of linear functionals in Banach spaces of measurable functions
Matematičeskie zametki, Tome 20 (1976) no. 5, pp. 733-739.

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In this note the existence of an operator extending linear functionals from a subspace to the whole space is studied. It is shown that under certain conditions on the Banach lattice of measurable functions and on a suitable subspace, there exists a unique extension operator. 
@article{MZM_1976_20_5_a12,
     author = {M. Sh. Braverman and G. Ya. Lozanovskii},
     title = {Extension of linear functionals in {Banach} spaces of measurable functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {733--739},
     publisher = {mathdoc},
     volume = {20},
     number = {5},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_5_a12/}
}
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M. Sh. Braverman; G. Ya. Lozanovskii. Extension of linear functionals in Banach spaces of measurable functions. Matematičeskie zametki, Tome 20 (1976) no. 5, pp. 733-739. http://geodesic.mathdoc.fr/item/MZM_1976_20_5_a12/