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It is shown explicitly that the correlation functions of Conformal
Field Theories(CFT) which posses the logarithmic operators are
invariant under the Borel subalgebra of
$\emph{W}_{\infty}-algebra$ constructed by tensor-operator algebra
of $sl(2,R)$. The general expression for three and four-point
correlation functions which posses logarithmic operators is
calculated.
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