Unformatted text preview: Let X = {1, 2, · · · , }, a countably inﬁnite alphabet.
Let PX = {1, 0, 0, · · · }, and let
Let PX = {1, 0, 0, · · · }, and let
9
8
>
>
⇢
>
>
<
=
1
1
1
,p
,··· , p
, 0, 0, · · · ..
PX n = 1 p
n
>
>
log n n log n
n log n
>
>
:
;

{z
}
n • As n ! 1,
• As n ! 1,
X
V (PX , PXn ) = X PX (i)
V (PX , PXn ) = i PX (i)
• However,
• However,
but i H ⇣ 2
PX n ( i )  = p
! 0.
2
log n
PX n...
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 Spring '14
 RaymondYeumg
 Information Theory, Mathematical analysis, Continuous function, Px, Binary logarithm, lim h

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