Abstract
We show that the causal structure determines a volume measurability up to sets of zero measure. In space-time manifolds this causal measurability, apart from sets of zero measure, agrees with the a priori four-dimensional Lebesgue measurability, provided the strong causality condition holds.
Similar content being viewed by others
References
Hawking, S. W., and Ellis, G. F. (1973).The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge).
Geroch, R. (1971). InGeneral Relativity and Cosmology, R. K. Sachs, ed. (Academic Press, New York).
Kolmogorov, A. N., and Fomin, S. V. (1960).Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, in Russian); Halmos, P. (1950).Measure Theory (D. Van Nostrand Co., Princeton, New Jersey); Choquet-Bruhat, Y., De Witt-Morett, C., and Dillard-Bleick, M. (1982).Analysis, Manifolds and Physics (North Holland Publ. Co., Amsterdam, New York, Oxford).
Kronheimer, E. (1971).Gen. Rel. Grav.,1, 261.
Kronheimer, E., and Penrose, R. (1967).Proc. Camb. Phil. Soc.,63, 481.
Carter, B. (1971).Gen. Rel. Grav.,1, 349.
Szabados, L. B. KFKI Report 1983-130.
Penrose, R. (1972). Techniques of Differential Topology in Relativity, No. 7 (SIAM, Philadelphia, Pennsylvania).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Szabados, L.B. Causal measurability in chronological spaces. Gen Relat Gravit 19, 1091–1100 (1987). https://doi.org/10.1007/BF00759145
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00759145