**Cramér's theorem** may also refer to another result of the same mathematician concerning the partial sums of a sequence of independent, identically distributed random variables, say *X*_{1}, *X*_{2}, *X*_{3}, …. It is well known, by the law of large numbers, that in this case the sequence

converges in probability to the mean of the probability distribution of *X _{k}*. Cramér's theorem in this sense states that the probabilities of "large deviations" away from the mean in this sequence decay exponentially with the

**rate**given by the

*Cramér function*, which is the Legendre transform of the cumulant-generating function of

*X*.

_{k}Read more about Cramér's Theorem: Slutsky's Theorem

### Other articles related to "theorem, theorems":

... In graph theory, the Robertson–Seymour

**theorem**(also called the graph minor

**theorem**) states that the undirected graphs, partially ordered by the graph minor ... defined by a finite set of forbidden minors, in the same way that Wagner's

**theorem**characterizes the planar graphs as being the graphs that do not have the complete graph K5 and the complete bipartite graph K3,3 ... The Robertson–Seymour

**theorem**is named after mathematicians Neil Robertson and Paul D ...

... The notion of a

**theorem**is very closely connected to its formal proof (also called a "derivation") ... is ABBA The only rule of inference (transformation rule) for is Any occurrence of "A" in a

**theorem**may be replaced by an occurrence of the string "AB ...

**Theorems**in are defined as those formulae which have a derivation ending with that formula ...

... algebra and functional analysis, the spectral

**theorem**is any of a number of results about linear operators or about matrices ... In broad terms the spectral

**theorem**provides conditions under which an operator or a matrix can be diagonalized (that is, represented as a diagonal ... In general, the spectral

**theorem**identifies a class of linear operators that can be modelled by multiplication operators, which are as simple as one can hope ...

... also Eigenfunction and Self-adjoint operator#Spectral

**theorem**The next generalization we consider is that of bounded self-adjoint operators on a Hilbert space ... of multiplication by t on L2, that is

**Theorem**... operator and There is also an analogous spectral

**theorem**for bounded normal operators on Hilbert spaces ...

... Friedman, Robertson Seymour (1987) showed that the following

**theorem**exhibits the independence phenomenon by being unprovable in various formal systems that are much stronger than ...

### Famous quotes containing the word theorem:

“To insure the adoration of a *theorem* for any length of time, faith is not enough, a police force is needed as well.”

—Albert Camus (1913–1960)