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:
“It is only a short step from exaggerating what we can find in the world to exaggerating our power to remake the world. Expecting more novelty than there is, more greatness than there is, and more strangeness than there is, we imagine ourselves masters of a plastic universe. But a world we can shape to our will ... is a shapeless world.”
—Daniel J. Boorstin (b. 1914)
“The best history is but like the art of Rembrandt; it casts a vivid light on certain selected causes, on those which were best and greatest; it leaves all the rest in shadow and unseen.”
—Walter Bagehot (1826–1877)