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An explicit form of the functional measure on  the factor space $Diff^{1}_{+}(S^{1})/SL(2,\textbf{R})$ is obtained thatmakes Schwarzian functional integrals calculus simpler and more transparent.

Functional integration over the factor-space $Diff^{1}_{+}(S^{1})/SL(2,\textbf{R}) $