## Weak compactness in the space of vector measures

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- by James K. Brooks PDF
- Bull. Amer. Math. Soc.
**78**(1972), 284-287

## References

- R. G. Bartle, N. Dunford, and J. Schwartz,
*Weak compactness and vector measures*, Canadian J. Math.**7**(1955), 289–305. MR**70050**, DOI 10.4153/CJM-1955-032-1 - Jürgen Batt and E. Jeffrey Berg,
*Linear bounded transformations on the space of continuous functions.*, J. Functional Analysis**4**(1969), 215–239. MR**0248546**, DOI 10.1016/0022-1236(69)90012-3 - James K. Brooks,
*On the existence of a control measure for strongly bounded vector measures*, Bull. Amer. Math. Soc.**77**(1971), 999–1001. MR**286971**, DOI 10.1090/S0002-9904-1971-12834-3
4. S. D. Chatterji, Weak convergence in certain special Banach spaces, MRC Technical Sum. Report #443, University of Wisconsin, Madison, Wis., 1963.
- N. Dinculeanu,
*Vector measures*, Hochschulbücher für Mathematik, Band 64, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. MR**0206189** - V. M. Dubrovskiĭ,
*On the basis of a family of completely additive functions of sets and on the properties of uniform additivity and equi-continuity*, Doklady Akad. Nauk SSSR (N. S.)**58**(1947), 737–740 (Russian). MR**0022894** - Nelson Dunford and Jacob T. Schwartz,
*Linear Operators. I. General Theory*, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR**0117523** - G. G. Gould,
*Integration over vector-valued measures*, Proc. London Math. Soc. (3)**15**(1965), 193–225. MR**174694**, DOI 10.1112/plms/s3-15.1.193 - A. Grothendieck,
*Sur les applications linéaires faiblement compactes d’espaces du type $C(K)$*, Canad. J. Math.**5**(1953), 129–173 (French). MR**58866**, DOI 10.4153/cjm-1953-017-4 - Solomon Leader,
*The theory of $L^p$-spaces for finitely additive set functions*, Ann. of Math. (2)**58**(1953), 528–543. MR**58126**, DOI 10.2307/1969752 - B. J. Pettis,
*On integration in vector spaces*, Trans. Amer. Math. Soc.**44**(1938), no. 2, 277–304. MR**1501970**, DOI 10.1090/S0002-9947-1938-1501970-8 - R. S. Phillips,
*On weakly compact subsets of a Banach space*, Amer. J. Math.**65**(1943), 108–136. MR**7938**, DOI 10.2307/2371776 - Pasquale Porcelli,
*Two embedding theorems with applications to weak convergence and compactness in spaces of additive type functions*, J. Math. Mech.**9**(1960), 273–292. MR**0124723**, DOI 10.1512/iumj.1960.9.59016 - J. J. Uhl Jr.,
*Orlicz spaces of finitely additive set functions*, Studia Math.**29**(1967), 19–58. MR**226395**, DOI 10.4064/sm-29-1-19-58

## Additional Information

- Journal: Bull. Amer. Math. Soc.
**78**(1972), 284-287 - MSC (1970): Primary 46G10; Secondary 28A55
- DOI: https://doi.org/10.1090/S0002-9904-1972-12960-4
- MathSciNet review: 0324408