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We prove versions of the Rubio de Francia extrapolation theorem in generalized Orlicz spaces. As a consequence, we obtain boundedness results for several classical operators as well as a Sobolev inequality in this setting. We also study complex interpolation in the same setting, and use it to derive a compact embedding theorem. Our results include as special cases classical Lebesgue and Sobolev space estimates, and their variable exponent and double phase growth analogs. Date: 12/03/2016. 2000doi:10.1090/tran/7155 fatcat:oskhkdmlv5hftgqz6bi6qmlobm