Almost surely information

In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (or Lebesgue measure...

converges almost completely, or almost in probability towards X. When Xn converges almost completely towards X then it also converges almost surely to X....

time will almost surely type any given text, including the complete works of William Shakespeare. In fact, the monkey would almost surely type every...

Almost periodic function - and Operators Almost all Almost surely Approximation List of mathematical jargon "Almost All Real Numbers are Transcendental -...

{ X n } {\displaystyle \{X_{n}\}} converges to X {\displaystyle X} almost surely, it means that the set of points O = { ω ∣ lim X n ( ω ) ≠ X ( ω ) }...

complement is of measure zero. In probability theory, the terms almost surely, almost certain and almost always refer to events with probability 1 not necessarily...

{\mathcal {N}}(0,u).} W {\displaystyle W} has almost surely continuous paths: W t {\displaystyle W_{t}} is almost surely continuous in t {\displaystyle t} . That...

of the following three conditions holds: (a) The stopping time τ is almost surely bounded, i.e., there exists a constant c ∈ N {\displaystyle \mathbb...

\alpha }} has almost surely pure point spectrum and exhibits Anderson localization. (It is known that almost surely can not be replaced by surely.) That the...

generally, "almost all" is sometimes used in the sense of "almost everywhere" in measure theory, or in the closely related sense of "almost surely" in probability...

{\displaystyle \mathbf {x} } and z {\displaystyle \mathbf {z} } , then almost surely we have m ~ M , n ( x , Θ 1 , … , Θ M ) = ∑ i = 1 n Y i K M , n ( x...

flips will almost surely converge to 1⁄2 as n approaches infinity. Although the proportion of heads (and tails) approaches 1⁄2, almost surely the absolute...

points have infinitely many intersections almost surely, but for dimensions higher than 5, they almost surely intersect only finitely often. The asymptotic...

"almost surely"—a central property of the Lebesgue integral. Basically, one says that an inequality like X ≥ 0 {\displaystyle X\geq 0} is true almost surely...

discovered to be exceptionally complex mathematically. The Wiener process is almost surely nowhere differentiable; thus, it requires its own rules of calculus...

the cumulative distribution function of a random variable which is almost surely 0. (See constant random variable.) In operational calculus, useful answers...

measurability theorem. A function f {\displaystyle f} is said to be almost surely separably valued (or essentially separably valued) if there exists a...

from an almost surely constant random variable, which may take other values, but only on events with probability zero. Constant and almost surely constant...

name for a clade). Therefore, in practice the name Liliopsida will almost surely refer to the usage as in the Cronquist system. In summary the monocotyledons...

) (almost surely) {\displaystyle {\frac {R_{1}+\cdots +R_{n}}{n}}\rightarrow {\frac {\mu (X)}{\mu (A)}}\quad {\text{(almost surely)}}} (See almost surely...

{1}{t}}Y_{t}={\frac {1}{\operatorname {E} [S_{1}]}}\operatorname {E} [W_{1}]} almost surely. Renewal processes additionally have a property analogous to the central...

decays almost surely if β is less than a critical value β* ≈ 0.70258, known as the Embree–Trefethen constant, and otherwise grows almost surely. They also...

the intersection of two almost sure events is almost sure. By definition, we conclude that g(Xn) converges to g(X) almost surely. Slutsky's theorem Portmanteau...