Complete Probability Space
A probability space is said to be a complete probability space if for all with and all one has . Often, the study of probability spaces is restricted to complete probability spaces.
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Famous quotes containing the words complete, probability and/or space:
“The Good of man is the active exercise of his soul’s faculties in conformity with excellence or virtue.... Moreover this activity must occupy a complete lifetime; for one swallow does not make spring, nor does one fine day; and similarly one day or a brief period of happiness does not make a man supremely blessed and happy.”
—Aristotle (384–322 B.C.)
“Only in Britain could it be thought a defect to be “too clever by half.” The probability is that too many people are too stupid by three-quarters.”
—John Major (b. 1943)
“If we remembered everything, we should on most occasions be as ill off as if we remembered nothing. It would take us as long to recall a space of time as it took the original time to elapse, and we should never get ahead with our thinking. All recollected times undergo, accordingly, what M. Ribot calls foreshortening; and this foreshortening is due to the omission of an enormous number of facts which filled them.”
—William James (1842–1910)