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The more e-books are available on the Internet, the less frequently people buy traditional books.
Is the second part of this sentence correct?
Yes it is correct.
I'd probably write, "The more e-books that are available, ..." There's a slight difference.
You can also omit the verb in the first clause in this case: "The more e-books available, the fewer traditional books people buy."
The following page gives some idea of when verbs can be left out with this constuction. If in doubt, use a verb.