Geodesic
Pettis integrability of Stone transforms
Matematičeskie zametki, Tome 60 (1996) no. 2, pp. 238-253

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Let $f$ be a bounded Pettis integrable function ranging in a Banach space $X$ (the range of the indefinite Pettis integral is separable). We consider Pettis integrability conditions for the Stone transform of $f$ and relate this problem to the regular oscillation condition for the family of functions $\{x^*f:x^*\in B(X^*)\}$, where $B(X^*)$ is the unit ball in $X^*$. 
@article{MZM_1996_60_2_a6,
     author = {V. I. Rybakov},
     title = {Pettis integrability of {Stone} transforms},
     journal = {Matemati\v{c}eskie zametki},
     pages = {238--253},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a6/}
}
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V. I. Rybakov. Pettis integrability of Stone transforms. Matematičeskie zametki, Tome 60 (1996) no. 2, pp. 238-253. http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a6/