Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On time-free functions


Author: Gideon Schwarz
Journal: Trans. Amer. Math. Soc. 167 (1972), 471-478
MSC: Primary 26A15; Secondary 39A15, 60G99
DOI: https://doi.org/10.1090/S0002-9947-1972-0293025-8
MathSciNet review: 0293025
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: By regarding as equivalent any two real-valued functions of a real variable that can be obtained from each other by a monotone continuous transformation of the independent variable, time-free functions are defined. A convenient maximal invariant is presented, and applied to some time-free functional equations.


References [Enhancements On Off] (What's this?)

  • [1] L. E. Dubins and D. A. Freedman, Random distribution functions, Bull. Amer. Math. Soc. 69 (1963), 548-551. MR 26 #7008. MR 0149522 (26:7008)
  • [2] L. E. Dubins and L. J. Savage, How to gamble if you must. Inequalities for stochastic processes, McGraw-Hill, New York, 1965. MR 38 #5276. MR 0236983 (38:5276)
  • [3] T. E. Harris, The theory of branching processes, Die Grundlehren der math. Wissenschaften, Band 119, Springer-Verlag, Berlin; Prentice-Hall, Englewood Cliffs, N. J., 1963. MR 29 #664. MR 0163361 (29:664)
  • [4] A. N. Kolmogorov and V. M. Tihomirov, $ \varepsilon $-entropy and $ \varepsilon $-capacity of sets in function spaces, Uspehi Mat. Nauk 14 (1959), no. 2 (86), 3-86. (Russian) MR 22 #2890. MR 0112032 (22:2890)
  • [5] B. McMillan, The basic theorems of information theory, Ann. Math. Statist. 24 (1953), 196-219. MR 14, 1101. MR 0055621 (14:1101h)
  • [6] L. S. Pontrjagin and L. G. Schnirelman, Sur un propriété métric de la dimension, Ann. of Math. 33 (1932), 156-162.
  • [7] G. de Rham, Sur une courbe plane, J. Math. Pures Appl. (9) 35 (1956), 25-42. MR 19, 842. MR 0090628 (19:842e)
  • [8] -, Sur quelques courbes definies par des équations fonctionnelles, Univ. e Politec. Torino, Rend. Sem. Mat. 16 (1956/57), 101-113. MR 20 #1733. MR 0095227 (20:1733)
  • [9] G. Schwarz, Time-free continuous processes, Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 1183-1188. MR 38 #5280. MR 0236987 (38:5280)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 26A15, 39A15, 60G99

Retrieve articles in all journals with MSC: 26A15, 39A15, 60G99


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0293025-8
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society