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:
“Man that is born of woman hath but a short time to live, and is full of misery. He cometh up, and is cut down, like a flower; he fleeth as it were a shadow, and never continueth in one stay.”
—Book Of Common Prayer, The. Burial of the Dead, “First Anthem,” (1662)
“The history of the genesis or the old mythology repeats itself in the experience of every child. He too is a demon or god thrown into a particular chaos, where he strives ever to lead things from disorder into order.”
—Ralph Waldo Emerson (1803–1882)