Continuous mapping theorem
In probability theory, the continuous mapping theorem states that continuous functions are limit-preserving even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps convergent sequences into convergent sequences: if xn → x then g(xn) → g(x). The continuous mapping theorem states that this will also be true if we replace the deterministic sequence {xn} with a sequence of random variables {Xn}, and replace the standard notion of convergence of real numbers “→” with one of the types of convergence of random variables.
Wikipage redirect
primaryTopic
Continuous mapping theorem
In probability theory, the continuous mapping theorem states that continuous functions are limit-preserving even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps convergent sequences into convergent sequences: if xn → x then g(xn) → g(x). The continuous mapping theorem states that this will also be true if we replace the deterministic sequence {xn} with a sequence of random variables {Xn}, and replace the standard notion of convergence of real numbers “→” with one of the types of convergence of random variables.
has abstract
In probability theory, the con ...... called the Mann–Wald theorem.
@en
Na teoria da probabilidade, o ...... i provado inicialmente por ().
@pt
在概率论中,连续映射定理指出,连续函数是具有保持极限的性质的 ...... 个定理第一次由证明,因此有时又被称作Mann–Wald定理。
@zh
Link from a Wikipage to an external page
Wikipage page ID
20,813,286
Wikipage revision ID
739,792,415
hypernym
type
comment
In probability theory, the con ...... nvergence of random variables.
@en
Na teoria da probabilidade, o ...... i provado inicialmente por ().
@pt
在概率论中,连续映射定理指出,连续函数是具有保持极限的性质的 ...... 个定理第一次由证明,因此有时又被称作Mann–Wald定理。
@zh
label
Continuous mapping theorem
@en
Teorema de Mann-Wald
@pt
连续映射定理
@zh