On the second dual of the space of continuous functions

On the second dual of the space of continuous functions
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Trans. Amer. Math. Soc. 86 (1957), 70-90

DOI: https://doi.org/10.1090/S0002-9947-1957-0090774-3

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References

Garrett Birkhoff, Lattice Theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. 25, American Mathematical Society, New York, N. Y., 1948. MR 0029876

Integration

Éléments de mathématique

J. Dieudonné, La dualité dans les espaces vectoriels topologiques, Ann. Sci. École Norm. Sup. (3) 59 (1942), 107–139 (French). MR 0011532
Jean Dieudonné, Sur le théorème de Lebesgue-Nikodym, Ann. of Math. (2) 42 (1941), 547–555 (French). MR 4719, DOI 10.2307/1968917
Jean Dieudonné, Sur le théorème de Lebesgue-Niko-dym. II, Bull. Soc. Math. France 72 (1944), 193–239 (French). MR 14580
Jean Dieudonné and Laurent Schwartz, La dualité dans les espaces $\scr F$ et $(\scr L\scr F)$, Ann. Inst. Fourier (Grenoble) 1 (1949), 61–101 (1950) (French). MR 38553
Alexandre Grothendieck, Sur la complétion du dual d’un espace vectoriel localement convexe, C. R. Acad. Sci. Paris 230 (1950), 605–606 (French). MR 40573
Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869

Topologie générale

Shizuo Kakutani, Concrete representation of abstract $(L)$-spaces and the mean ergodic theorem, Ann. of Math. (2) 42 (1941), 523–537. MR 4095, DOI 10.2307/1968915
Shizuo Kakutani, Concrete representation of abstract $(M)$-spaces. (A characterization of the space of continuous functions.), Ann. of Math. (2) 42 (1941), 994–1024. MR 5778, DOI 10.2307/1968778
Hidegorô Nakano, Linear topologies on semi-ordered linear spaces, J. Fac. Sci. Hokkaido Univ. Ser. I. 12 (1953), 87–104. MR 0056851
G. T. Roberts, Topologies in vector lattices, Proc. Cambridge Philos. Soc. 48 (1952), 533–546. MR 50873, DOI 10.1017/s0305004100076295