Transform Probability Distribution P to Uniform Distribution

[mjpam]

I vaguely remember a theorem that says, given a probability distribution P, there exists a transform T from P to the uniform (I think discrete or continuous) distribution.

Is this true?

Can anyone provide me with an online citation?

 

[EnumaElish]

Could this be it:
http://en.m.wikipedia.org/wiki/Inverse_transform_sampling?wasRedirected=true

 

[mjpam]

Could this be it:
http://en.m.wikipedia.org/wiki/Inverse_transform_sampling?wasRedirected=true

That loos familiar, but, in my vague recollection, the continuity of the probability distribution was not specified.

 

[bpet]

The uniform distribution can be transformed to any other distribution via the quantile function (i.e. the inverse CDF) but for the reverse the distribution must be continuous (a continuous interval can be mapped to a point but not vice-versa).

 

[mjpam]

Would it be true to say thatm given a discrete probability distribution, P_{D}, and the discrete uniform distribution, U_{D} there exists transform
T : P_{D} \to U_{D} and its inverse T^{-1} is well-deifned?