The -PIP and integrability

of a single function

Author:
Gunnar F. Stefánsson

Journal:
Proc. Amer. Math. Soc. **124** (1996), 539-542

MSC (1991):
Primary 46G10, 28B05

DOI:
https://doi.org/10.1090/S0002-9939-96-03105-X

MathSciNet review:
1301529

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Two examples are given that answer in the negative the following question asked by E. M. Bator: If is bounded and weakly measurable and for each in there is a bounded sequence in such that a.e., does it follow that is Pettis integrable?

**1**E. M. Bator,*Pettis integrability and equality of the norms of the weak* integrable and the Dunford integral*, Proc. Amer. Math. Soc.**95**(1985), 265--270. MR**87a:46074****2**K. Musial and G. Plebanek,*Pettis integrability and equality of the norms of the weak* integral and the Dunford integral*, Hiroshima Math. J.**19**(1989), 329--332. MR**91c:46064****3**R. Phillips,*Integrability in a convex linear topological space*, Trans. Amer. Math. Soc.**47**(1940), 114--145. MR**2:103c****4**G. F. Stefánsson,*Pettis integrability*, Ph.D. thesis, Pennsylvania State University, 1989.**5**M. Talagrand,*Pettis integral and measure theory*, Mem. Amer. Math. Soc., no. 307, 1984. MR**86j:46042**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
46G10,
28B05

Retrieve articles in all journals with MSC (1991): 46G10, 28B05

Additional Information

**Gunnar F. Stefánsson**

Affiliation:
Department of Mathematics, Pennsylvania State University, Altoona Campus, Altoona, Pennsylvania 16601

Email:
gfs@math.psu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03105-X

Keywords:
$\mathrm{weak}^*$ integral,
Pettis integral

Received by editor(s):
July 14, 1993

Received by editor(s) in revised form:
September 7, 1994

Communicated by:
Dale Alspach

Article copyright:
© Copyright 1996
American Mathematical Society