an:00474681
Zbl 0798.46042
Musia??, Kaziemierz
Topics in the theory of Pettis integration
EN
Rend. Ist. Mat. Univ. Trieste 23, 177-262 (1991).
00015881
1991
j
46G10 28B05 46G12
measures in a normed space; limit theorems; Pettis integral; strongly measurable functions; scalarly bounded functions; weak Radon-Nikodym property of conjugate Banach spaces
This paper is based on lectures presented at the School on Measure Theory and Real Analysis (Grado (Italy), 1991/92). It is divided into the following chapters:
1. Preliminaries, 2. Measures in a normed space, Measurable functions, 4. Pettis integral, 5. Integrability of strongly measurable functions, 6. Criteria for Pettis integrability, 7. Integration of scalarly bounded functions, 8. Limit theorems, 9. Approximation by simple functions -- the compact case, 10. Approximation by simple functions -- the separable case, 11. The weak Radon-Nikodym property -- the general case, 12. The weak Radon-Nikodym property of conjugate Banach spaces, 13. Comments, 14. References.
The paper is an excellently written exposition of the main topics in the theory of Pettis integration. It contains 40 open problems. The paper is of interest for the experts as well as for the beginners in this field; it is selfcontained and requires from the reader only the basic facts in the theory of Banach spaces and in measure theory.
H.Weber (Potenza)