Short History
The theory of standard probability spaces was started by von Neumann in 1932 and shaped by Vladimir Rokhlin in 1940. For modernized presentations see (Haezendonck 1973), (de la Rue 1993), (Itô 1984, Sect. 2.4) and (Rudolf 1990, Chapter 2).
Nowadays standard probability spaces may be (and often are) treated in the framework of descriptive set theory, via standard Borel spaces, see for example (Kechris 1995, Sect. 17). This approach is based on the isomorphism theorem for standard Borel spaces (Kechris 1995, Theorem (15.6)). An alternate approach of Rokhlin, based on measure theory, neglects null sets, in contrast to descriptive set theory. Standard probability spaces are used routinely in ergodic theory,
Read more about this topic: Standard Probability Space
Famous quotes containing the words short and/or history:
“Give a scientist a problem and he will probably provide a solution; historians and sociologists, by contrast, can offer only opinions. Ask a dozen chemists the composition of an organic compound such as methane, and within a short time all twelve will have come up with the same solution of CH4. Ask, however, a dozen economists or sociologists to provide policies to reduce unemployment or the level of crime and twelve widely differing opinions are likely to be offered.”
—Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)
“Jesus Christ belonged to the true race of the prophets. He saw with an open eye the mystery of the soul. Drawn by its severe harmony, ravished with its beauty, he lived in it, and had his being there. Alone in all history he estimated the greatness of man.”
—Ralph Waldo Emerson (1803–1882)