In mathematics, exponential equivalence of measures is how two sequences or families of probability measures are "the same" from the point of view of large deviations theory.

Definition

be a metric space and consider two one-parameter. These two families are said to be exponentially equivalent if there exist

• ,

• ,

such that

• -law (i.e. the push-forward measure,

• -measurable event, i.e.

• ,

are also said to be exponentially equivalent.

Properties

with good rate function.

References

• (See section 4.2.2)