Pacific Journal of Mathematics

Invariant extensions of linear functionals, with applications to measures and stochastic processes.

E. J. McShane, R. B. Warfield, Jr., and V. M. Warfield

Article information

Source
Pacific J. Math., Volume 28, Number 1 (1969), 121-142.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102983615

Mathematical Reviews number (MathSciNet)
MR0239398

Zentralblatt MATH identifier
0172.15601

Subjects
Primary: 46.06
Secondary: 28.00

Citation

McShane, E. J.; Warfield, R. B.; Warfield, V. M. Invariant extensions of linear functionals, with applications to measures and stochastic processes. Pacific J. Math. 28 (1969), no. 1, 121--142. https://projecteuclid.org/euclid.pjm/1102983615


Export citation

References

  • [1] R. P. Agnew, and A. P. Morse, Extensions of linear functionals, with applications to limits, integrals, measures and densities, Ann. of Math. (2) 39 (1938), 20-30.
  • [2] H. Cramer, On the theory of stationaryrandom processes, Ann. of Math. (2) 41 (1940), 215-230.
  • [3] Mahlon M. Day, Means for the bounded functions and ergodicity of the bounded re- presentations of semigroups, Trans. Amer. Math. Soc. 69 (1950),276-291.
  • [4] J. L. Doob, Stochastic processes, John Wiley and Sons, Inc., New York, 1953.
  • [5] V. L. Klee, Invariant extension of linear functionals,Pacific J. Math. 4 (1954), 37-46.
  • [6] M. G. Krein, Sur le probleme du prolongement des fonctions Hermitiennes positives et continues, Comptes Rendus de Acad. des Sci. de URSS 2 (1940), 17-22.
  • [7] N. M. Kryloff and N. N. Bogoliuboff, La theorie generale de la mesure et son ap- plication a etude des systemes dynamiques de la mecanique non lineaire, Ann. of Math. (2) 38 (1937),65-113.
  • [8] M., Loeve, Probability theory, D. van Nostrand Co., Inc., Princeton, 1960.
  • [9] V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of differential equa- tions, Princeton, 1960.
  • [10] K. R. Parthasarathy and S. R. S. Varadhan, Extension of stationarystochastic processes, Theory of Prob. and Its Appl. 9 (1964), 65-71.
  • [11] A. J. Schwartz, On certain conditions for the existence of invariant linear func- tionals, Proc. Amer. Math. Soc. 12 (1961),857-861.
  • [12] J. von Neumann, Zur allgemeine theorie des masses, Fund. Math. 13 (1929), 73- 116.