Ordered Sample Space

Example(s):
- {1 < 2 < 3 < 4 < 5 < 6}, from a Dice Roll Experiment.
- {0... < 0.1 … < 102.2 < … ∞}, from a Lifetime Experiment.
See: Unordered Sample Space.

References

Sun Yong Kim, Iickho Song, Jae Cheol Son, and Sangyoub Kim. (1995). “Performance Characteristics of the Fuzzy Sign Detector.” In: Fuzzy Sets and Systems, 74
- Proof of Theorem 1. Let u₊ and u_- be the number of k₊s and k_-s in the observation [math]\displaystyle{ k }[/math], respectively, $Q$ = {t_j} be the ordered sample space with elements arranged in the decreasing order of corresponding value of the FS test statistic or equivalently in the decreasing order of the value (w+ — u_ ), and tj be the 7th element of r.

Yuri Gurevich. (1991). “Average Case Completeness.” In: Journal of Computer and System Sciences, 42(3). doi:0.1016/0022-0000(91)90007-R.
- We will consider only finite or infinite countable sample spaces, i.e., probability spaces. The function that assigns probabilities to sample points is the probability function. If μ is a probability function and [math]\displaystyle{ X }[/math] is a collection of sample points then the μ-probability of the event [math]\displaystyle{ X }[/math] will be denoted μ(X); in other words, μ(X) = P x2X μ(x). The letters μ and ν are reserved for probability functions. If μ(x) is a probability function on an ordered sample space then μ^*(x) = Sigma y<x μ(y) is the corresponding probability distribution. A probability function μ is positive if every value of μ is positive. The restriction μ|X of a probability function μ to a set [math]\displaystyle{ X }[/math] of sample points with μ(x) > 0 is the probability function proportional to μ on [math]\displaystyle{ X }[/math] and zero outside X.