Typical-set cardinality bounds
= Typical-set cardinality bounds
For a <typical set> of probability at least $1-\delta$,
$$
(1-\delta)2^{n(H-\varepsilon)}\leq|T_\varepsilon^{(n)}|\leq2^{n(H+\varepsilon)}.
$$
The upper bound sums the lower probability bound for each word; the lower bound sums the upper probability bound and uses the set's total probability. These bounds turn the <asymptotic equipartition property> into exponential estimates of source-coding dimension.