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Following the definition of parabolic rational functions and in view of the behavior of transcendental meromorphic functions, we give the definition of parabolic transcendental meromorphic functions. We discuss their dynamical behavior and prove the existence of conformal measures and invariant measures over their Julia sets, thus extending Denker and Urbański's work on parabolic rational functions. However, our method for proving the existence of the conformal measures differs in that we usedoi:10.2140/pjm.2011.250.487 fatcat:l3o24hxzrzdbxldkixl7ppf6vy