An Etymological Dictionary of the German Language/Müller
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Müller, m., ‘miller,’ from MidHG. mülner, mülnœre, n. (ln is preserved in the surname Müllner, in other cases it is represented by ll), OHG. mûlinâri, m., ‘miller.’ A derivative of Mühle (OHG. mulîna), or borrowed directly from MidLat. molinarius (Ital. mulinaro, Fr. meunier), ‘miller.’ See Mühle.