Notes on Cambridge Maths

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Distribution Type Class

Let be a Distribution Type on finite alphabet .
The type class is defined as:

i.e. the set of all strings which generate the same empirical distribution.

Proposition

For any type on an alphabet of size we have:

Lemma

The most likely type class under is :

Proposition

For any Distribution Type over an alphabet of size
and for any distribution on we have:

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