Geodesic
Adjoint functions and integrals
Izvestiya. Mathematics , Tome 6 (1972) no. 2, pp. 429-443

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In this paper it is proved that $A$-integrals and $B$-integrals are inconsistent with the Denjoy–Hincin integral of functions which are adjoint to a summable function. Furthermore, the paper establishes nonadditivity of the $B$-integrals on an interval. 
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     author = {T. P. Lukashenko},
     title = {Adjoint functions and integrals},
     journal = {Izvestiya. Mathematics },
     pages = {429--443},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a6/}
}
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T. P. Lukashenko. Adjoint functions and integrals. Izvestiya. Mathematics , Tome 6 (1972) no. 2, pp. 429-443. http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a6/