Von Neumann on measure and ergodic theory
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- by Paul R. Halmos PDF
- Bull. Amer. Math. Soc. 64 (1958), 86-94
References
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1. G. D. Birkhoff, Proof of the ergodic theorem, Proc. Nat. Acad. Sci. vol. 17 (1931) pp. 656-660.
2. G. D. Birkhoff and B. O. Koopman, Recent contributions to the ergodic theory, Proc. Nat. Acad. Sci. vol. 18 (1932) pp. 279-282.
3. B. O. Koopman, Hamiltonian systems and transformations in Hilbert space, Proc. Nat. Acad. Sci. vol. 17 (1931) pp. 315-318.
4. John von Neumann, Die Zerlegung eines Intervalles in abzählbar viele kongruente Teilmengen, Fund. Math. vol. 11 (1928) pp. 230-238.
5. John von Neumann, Zur allgemeinen Theorie des Masses, Fund. Math. vol. 13 (1929) pp. 73-116.
6. John von Neumann, Zusatz zur Arbeit "Zur allgemeinen Theorie des Masses", Fund. Math. vol. 13 (1929) p. 333.
- John von Neumann, A numerical method to determine optimum strategy, Naval Res. Logist. Quart. 1 (1954), 109–115. MR 63776, DOI 10.1002/nav.3800010207 8. John von Neumann, Proof of the quasi-ergodic hypothesis, Proc. Nat. Acad. Sci. vol. 18 (1932) pp. 70-82. 9. John von Neumann and B. O. Koopman, Dynamical systems of continuous spectra, Proc. Nat. Acad. Sci. vol. 18 (1932) pp. 255-263. 10. John von Neumann, Physical applications of the ergodic hypothesis, Proc. Nat. Acad. Sci. vol. 18 (1932) pp. 263-266.
- J. von Neumann, Einige Sätze über messbare Abbildungen, Ann. of Math. (2) 33 (1932), no. 3, 574–586 (German). MR 1503077, DOI 10.2307/1968536
- J. von Neumann, Zur Operatorenmethode in der klassischen Mechanik, Ann. of Math. (2) 33 (1932), no. 3, 587–642 (German). MR 1503078, DOI 10.2307/1968537
- J. von Neumann, Zusätze zur Arbeit “zur Operatorenmethode...”, Ann. of Math. (2) 33 (1932), no. 4, 789–791 (German). MR 1503096, DOI 10.2307/1968225
- J. V. Neumann, Zum Haarschen Maßin topologischen Gruppen, Compositio Math. 1 (1935), 106–114 (German). MR 1556880 15. John von Neumann and M. H. Stone, The determination of representative elements in the residual classes of a Boolean algebra, Fund. Math. vol. 25 (1935) pp. 353-378. 16. John von Neumann, The uniqueness of Haar’s measure, Mat. Sbornik vol. 1 (1936) pp. 721-734.
- Israel Halperin, The extraordinary inspiration of John von Neumann, The legacy of John von Neumann (Hempstead, NY, 1988) Proc. Sympos. Pure Math., vol. 50, Amer. Math. Soc., Providence, RI, 1990, pp. 15–17. MR 1067747, DOI 10.1090/pspum/050/1067747
- Paul R. Halmos and John von Neumann, Operator methods in classical mechanics. II, Ann. of Math. (2) 43 (1942), 332–350. MR 6617, DOI 10.2307/1968872
- John von Neumann, Functional Operators. I. Measures and Integrals, Annals of Mathematics Studies, No. 21, Princeton University Press, Princeton, N. J., 1950. MR 0032011
Additional Information
- Journal: Bull. Amer. Math. Soc. 64 (1958), 86-94
- DOI: https://doi.org/10.1090/S0002-9904-1958-10203-7
- MathSciNet review: 0097294