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On the asymptotic rate of non-ergodic information sources. (English) Zbl 0245.94013

MSC:
94A15 Information theory (general)
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References:
[1] P. R. Halmos: Measure theory. New York 1950. · Zbl 0040.16802
[2] A. I. Khinchin: Mathematical foundations of information theory. Dover Publications, New York 1957. · Zbl 0088.10404
[3] N. Kryloff N. Bogoliouboff: La théorie générale de la mesure dans son application à l’étude des systèmes dynamique de la mécanique non linéaire. Ann. of Math. 38 (1937), 65-113. · JFM 63.1002.01
[4] B. McMillan: The basic theorems of information theory. Ann. Math. Stat. 24 (1953), 196-219. · Zbl 0050.35501
[5] J. C. Oxtoby: Ergodic sets. Bull. Amer. Math. Soc. 58 (1952), 116-136. · Zbl 0046.11504
[6] K. R. Parthasarathy: On the integral representation of the rate of transmission of a stationary channel. Illinois Journ. of Math. 5 (1961), 2, 299-305. · Zbl 0100.33903
[7] K. R. Parthasarathy: A note on McMillan’s theorem for countable alphabets. Transact. Third Prague Conf. on Inform. Theory etc., Prague 1964, 541-543. · Zbl 0199.21401
[8] K. R. Parthasarathy: Effective entropy rate and transmission of information through channels with additive random noise. Manuscript, 1962. · Zbl 0119.34003
[9] A. Perez: Notions généralizées d’incertitude, d’entropie et d’information. Transact. First Prague Conf. on Inform. Theory etc., Prague 1957, 183-208.
[10] A. Perez: Sur la théorie de l’information dans le cas d’un alphabet abstrait. Transact. First Prague Conf. on Inform. Theory etc., Prague 1957, 209-243. · Zbl 0106.33102
[11] A. Perez: Extensions of Shannon-McMillan’s limit theorem to more general stochastic processes. Transact. Third Prague Conf. on Inform. Theory etc., Prague 1964, 545-574. · Zbl 0126.35703
[12] V. A. Rohlin: New progress in the theory of transformation with invariant measure. (In Russian). Usp. matem. nauk 15 (1960), 3-26.
[13] C. E. Shannon: A mathematical theory of communication. Bell System Tech. Journ. 27 (1948), Part I, 379-423. · Zbl 1154.94303
[14] I. G. Sinal: On the flows with finite entropy. (In Russian). Dokl. Akad. Nauk 125 (1959), 6, 1200-1202. · Zbl 0117.35202
[15] K. Winkelbauer: On discrete information sources. Transact. Third Prague Conf. on Inform. Theory etc., Prague 1964, 765-830. · Zbl 0126.35702
[16] K. Winkelbauer: Axiomatic definition of channel capacity and entropy rate. Transact. Fourth Prague Conf. on Inform. Theory etc., Prague 1967, 661-705.
[17] K. Winkelbauer: Channels with finite past history. Transact. Second Prague Conf. on Inform. Theory etc., Prague 1960, 685-831. · Zbl 0161.16904
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