References: R. B. Griffiths, Consistent Histories and the Interpretation of Quantum Mechanics, Journal of statistical Physics., 36(12):219-272(1984)
M. Gell-Mann and J. B. Hartle, in Complexity, Entropy and the Physics of Information, edited by W. Zurek, Santa Fe Institute Studies in the Sciences of Complexity Vol. VIII, Addison-Wesley, Reading, 1990. Also in Proceedings of the $3$rd International Symposion on the Foundations of Quantum Mechanics in the Light of New Technology, edited by S. Kobayashi, H. Ezawa, Y. Murayama and S. Nomura, Physical Society of Japan, Tokyo, 1990
R. B. Griffiths, Phys. Rev. Lett. 70, 2201 (1993)
R. Omn\`es, Rev. Mod. Phys. 64, 339 (1992)
In this approach serious problems arise. This is best pointed out in: B. d'Espagnat, J. Stat. Phys. 56, 747 (1989)
F. Dowker und A. Kent, On the Consistent Histories Approach to Quantum Mechanics, University of Cambridge Preprint DAMTP/94-48, Isaac Newton Institute for Mathematical Sciences Preprint NI 94006, August 1994.