Order theoretic foundations of integration. (English) Zbl 0111.25605
References:
| [1] | Alfsen, E. M.: On a general theory of integration based on order. Math. Scand.6, 67-79 (1958). · Zbl 0083.27401 |
| [2] | ?? A remark concerning the article, On a general theory of integration based on order. Math. Scand.7, 106-108 (1959). · Zbl 0173.05202 |
| [3] | ?? The optimal Lebesgue-Radon-Nikodym Inequality. Bull. Am. Math. Soc.65, No. 3, 230-233 (1962). · Zbl 0129.27103 · doi:10.1090/S0002-9904-1962-10757-5 |
| [4] | Bauer, H.: Reguläre und singuläre Abbildungen eines Verbandes in einen vollständigen Vektorverband, welche der Funktionalgleichungf(x?y)+f(x?y),=f(x)+f(y), genügen. J. reine angew. Math.194, 141-179 (1955). · Zbl 0065.01705 · doi:10.1515/crll.1955.194.141 |
| [5] | Birkhoff, G.: Lattice theory. Am. Math. Soc. Coll. Publ. XXV, New York 1948. · Zbl 0033.10103 |
| [6] | Bourbaki, N.: Intégration. Act. Sci. et Ind.1175. Paris 1952. |
| [7] | – Topologie générale, ch. IX. Act. Sci. et Ind.1045. Paris 1948. |
| [8] | Choquet, G.: Theory of capacities. Ann. Inst. Fourier5, 131-292 (1953-54). |
| [9] | Cristescu, R.: Spatii liniare ordonate. Acad. Rep. Pop. Romine. Bibl. Mat. III. Bucarest 1959. · Zbl 0090.08703 |
| [10] | Daniell, P. F.: A general form of integral. Ann. Math.19, 279-294 (1917-18). · JFM 46.0395.01 · doi:10.2307/1967495 |
| [11] | Dieudonné, J.: Sur le théoreme deLebesgue-Nikodym. Ann. Math. (2)42, 547-555 (1941). · Zbl 0027.11201 · doi:10.2307/1968917 |
| [12] | ?? Sur le théoreme deLebesgue-Nikodym. II. Bull. soc. Math. France72, 193-239 (1944);74, 66-68 (1946). · Zbl 0060.26306 |
| [13] | Edwards, R. E.: A theory ofRadon measures on locally compact spaces. Acta Math.89, 133-164 (1953). · Zbl 0050.05702 · doi:10.1007/BF02393005 |
| [14] | Halmos, P. R.: Measure theory. New York: Van Nostrand 1950. · Zbl 0040.16802 |
| [15] | Hahn, H., andA. Rosenthal: Set functions. Albuquerque: Univ. of New Mexico Press 1948. |
| [16] | Hildebrandt, T. H.: Definitions of Stieltjes integrals of the Riemann type. Am. Math. Monthly45, 265-278 (1938). · Zbl 0019.05604 · doi:10.2307/2302540 |
| [17] | Jacobson, N.: Lectures in abstract algebra. New York: Van Nostrand 1951. · Zbl 0044.26002 |
| [18] | Kakutani, S.: Concrete representations of abstract (L)-spaces and the mean ergodic theorem. Ann. Math. (2)41, 174-206 (1940). · Zbl 0022.31802 · doi:10.2307/1968825 |
| [19] | Kantorovitch, L.: Lineäre halbgeordnete Räume. Mat. Sbornik2, (44), 121-168 (1937). · JFM 63.0353.01 |
| [20] | Kappos, D. A., u.A. Mallios: Der Integralbegriff ino-topologischen Verbänden. Bull. Soc. Math. de Grece, N.S. 1, Fasc.1, 98-105 (1960). · Zbl 0112.28502 |
| [21] | Krickeberg, K.: Extreme Derivierte von Zellenfunktionen in Booleschen ?-Algebren und ihre Integration. Sitzber. Bay. Akad. Wiss.1955, 217-279. · Zbl 0072.04501 |
| [22] | ?? Convergence of martingales with a directed index set. Trans. Am. Math. Soc.83, 313-337 (1956). · Zbl 0083.27501 · doi:10.1090/S0002-9947-1956-0091328-4 |
| [23] | ?? Stochastische Konvergenz von Semimartingalen. Math. Z.66, 470-486 (1957). · Zbl 0083.27601 · doi:10.1007/BF01186623 |
| [24] | Lebesgue, H.: Leçons sur l’intégration et la recherche des fonctions primitives. Paris: Gauthier Villars 1928 (Second edition). · JFM 54.0257.01 |
| [25] | Loomis, L.: An introduction to abstract harmonic analysis. New York: Van Nostrand 1953. · Zbl 0052.11701 |
| [26] | McShane, E.: Remark concerning integration. Proc. Nat. Acad. Sci.35, 46-49 (1949). · Zbl 0032.15002 · doi:10.1073/pnas.35.1.46 |
| [27] | ?? Order preserving maps and integration processes. Ann. Math. Studies31. Princeton: Princeton Univ. Press 1953. · Zbl 0051.29301 |
| [28] | Maeda, F.: Kontinuierliche Geometrien. Berlin-Göttingen-Heidelberg: Springer-Verlag 1958. |
| [29] | Mallios, A.: Isotone modular mappings in lattices. (In Greek). Bull. Soc. Math. de Grèce, N.S. 1, Fasc.2, 1-45 (1960). |
| [30] | Makano, H.: Ergodic theory in semi-ordered linear spaces. Ann. Math.49, 538-556 (1948). · Zbl 0032.35901 · doi:10.2307/1969044 |
| [31] | Ore, O.: On the foundations of abstract algebra. Ann. Math.36, 406-437 (1935). · JFM 61.0111.09 · doi:10.2307/1968580 |
| [32] | Riesz, F.: Sur quelques notions fondamentales dans de la théorie générale des operateurs lineaires. Ann. Math. (2)41, 174-206 (1940). · Zbl 0022.31802 · doi:10.2307/1968825 |
| [33] | Stone, M. H.: Notes on integration I?II. Proc. Nat. Acad. Sci.34, 336-342, 447-455 (1948). · Zbl 0031.01402 · doi:10.1073/pnas.34.7.336 |
| [34] | Urysohn, P. S.: Sur les classes (L) deM. Fréchet. Ens. de Math.25, 77-83 (1926). · JFM 52.0582.03 |
| [35] | Yosida, K., andE. Hewitt: Finitely additive measures. Trans. Am. Math. Soc.72, 46-66 (1952). · Zbl 0046.05401 · doi:10.1090/S0002-9947-1952-0045194-X |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
