Pettis decomposition for universally scalarly measurable functions

Author:
Elizabeth M. Bator

Journal:
Proc. Amer. Math. Soc. **104** (1988), 795-800

MSC:
Primary 28B05; Secondary 46G10

DOI:
https://doi.org/10.1090/S0002-9939-1988-0964859-6

MathSciNet review:
964859

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if is a compact Hausdorff space, is a Banach space, and is bounded and universally scalarly measurable, then is -Pettis decomposable for every Radon measure on .

**[1]**E. M. Bator,*The Pettis Integral and the equality of the norms of the Dunford integral and the weak* integral*, Proc. Amer. Math. Soc.**95**(1985), 265-270. MR**801336 (87a:46074)****[2]**-,*A decomposition of bounded scalarly measurable functions taking their ranges in dual Banach spaces*, Proc. Amer. Math. Soc.**102**(1988), 850-854. MR**934855 (89i:46050)****[3]**E. M. Bator, P. W. Lewis, and D. Race,*Some connections between Pettis integration and operator theory*, Rocky Mountain Math. J.**17**(1985), 265-270. MR**923739 (89b:46060)****[4]**J. Bourgain,*Martingales in conjugate Banach spaces*(Unpublished preprint).**[5]**D. H. Fremlin,*Pointwise compact sets of measurable functions*, Manuscripta Math.**15**(1975), 219-242. MR**0372594 (51:8801)****[6]**R. S. Phillips,*Integration in a convex linear topological space*, Trans. Amer. Math. Soc.**47**(1940), 114-145. MR**0002707 (2:103c)****[7]**L. H. Riddle and E. Saab,*On functions that are universally Pettis integrable*, Illinois J. Math.**29**(1985), 509-531. MR**786735 (86i:28012)****[8]**L. H. Riddle, E. Saab, and J. J. Uhl Jr.,*Sets with the weak Radon-Nikodym property in dual Banach spaces*, Indiana Univ. Math. J.**32**(1983), 527-540. MR**703283 (84h:46028)****[9]**H. P. Rosenthal,*A characterization of Banach spaces containing*, Proc. Nat. Acad. Sci. U.S.A.**71**(1974), 2411-2413. MR**0358307 (50:10773)****[10]**M. Talagrand,*Pettis integral and measure theory*, Mem. Amer. Math. Soc., No. 307 (1984). MR**756174 (86j:46042)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
28B05,
46G10

Retrieve articles in all journals with MSC: 28B05, 46G10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0964859-6

Keywords:
Banach space,
Pettis integral,
universally scalarly measurable,
Bourgain property

Article copyright:
© Copyright 1988
American Mathematical Society