The general statistical problem in physics and the theory of probability

D. Bohm; W. Schützer

doi:10.1007/bf02744278

journal article Jan 01, 1955

The general statistical problem in physics and the theory of probability

D. Bohm W. Schützer

Il Nuovo Cimento Vol. 2 No. S4 pp. 1004-1047 · Springer Science and Business Media LLC

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References

18

[1]

After we had finished this work. Prof. Mario Schönberg; called our attention to the fact that son e of the ideas on chance and probability appearing in this paper had already been suggested by Couarnot (Erosition de la théorie des chances et des prohabilitéx, Paris, 1843).

[2]

The importance of the relative frequency in connection with probability was first recognized byEllis (On the Foundations of the Theory of Probabilities, inTram. of Camb. Phil. Soc,8, 1–6 (1844)), (paper read in 1842), and then by Cournot(Exposition de la théorie des chances et des probabilté s, Paris, 1843). However, neither ofthese authors fully eliminated the subjective point of view, Venn(The Logic of Chance, London and New York, 1866) advocated systematically a pure frequency interpretation.

[3]

R. von Mises:Wahrscheinlichkeit, Statistik und Wahrheit, dritte Aufl. (Wien, 1951). 10.1007/978-3-7091-2067-5

[4]

J. Ville:Étude Critique de Ja Notion de Collectif (Paris, 1939).

[5]

A. Kolmogoroff:Grundbegriffe der Wahrscheinlichkeitsrechnung, inErg. d. Math.,2, n. 3.

[6]

P. andT. Ehrenfest:Encyklop. der Math. Wiss.,4, 4 (Leipzig, 1907–1914)

[7]

P. andT. Ehrenfest:Encyclopedie des Sciences Mathématiques,4, 2, Supplément II.

[8]

the proof of the central limit theorem inA. I. Khinchin:Statistical Mechanics (New York, 1949)

[9]

A. I, Khinchin:Statistical Mechanics (New York, 1949).

[10]

Thus, as a consequence of a theorem proved byPoincaré Acta Math.,13, 67 (1800)

[11]

A. I. Khinchin:Mathematical Foundations of Statistical Mechanics, sec.13

[12]

P. Hertz:Weber-Gans, inRepertorium d. Physik, Bd.1, 2 (Leipzig, 1916);T. Levi-Civita:Drei Vorlesungen über adiabalische Inrarianten, inAbh. d. Math. Se minars Hamburg,6. 323 (1928).

[13]

M. Schönberg:Nuovo Cimento,10, 419 (1953) where a discussion is given of the problem of taking averages in a non equilibrium process. 10.1007/bf02781980

[14]

H. Weyl:Math. Ann.,77, 313 (1916). 10.1007/bf01475864

[15]

H. Poinczré:Calcul des Probabilités (Paris, 1912).

[16]

M. Katz andH. Steinhaus:Studia Mathematica,6, 59 (1936). 10.4064/sm-6-1-59-66

[17]

H. G. Goldstein:Classical Mechanies (1952), Chap. 10

[18]

R. C. Tolman:The Principles of Statistical Mechanics, (Oxford, 1950), Chap. IX.

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Published: Jan 01, 1955
Vol/Issue: 2(S4)
Pages: 1004-1047
License: View

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D. Bohm, W. Schützer (1955). The general statistical problem in physics and the theory of probability. Il Nuovo Cimento, 2(S4), 1004-1047. https://doi.org/10.1007/bf02744278

The general statistical problem in physics and the theory of probability

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