Repeatable measurements in quantum theory: their role and feasibility 1 Paul Busch 2 Department of Physics, Harvard University, Cambridge, MA 02138, USA E-mail: pbusch@string.harvard.edu Marian Grabowski Institute of Physics, Nicolaus Copernicus University, PL-87-100 Toru´ n, Poland E-mail: magrab@vm.cc.torun.edu.pl Pekka J. Lahti Department of Physics, University of Turku, SF-20500 Turku, Finland E-mail: peklahti@sara.utu.fi Abstract Recent advances in experimental quantum physics call for a careful reconsideration of the meas- urement process in quantum mechanics. In this paper we describe the structure of the ideal meas- urements and their status among the repeatable measurements. Then we provide an exhaustive account of the interrelations between repeatability and the apparently weaker notions of of value reproducible or first-kind measurements. We demonstrate the close link between repeatable meas- urements and discrete observables and show how the ensuing measurement limitations for continuous observables can be lifted in a way that is in full accordance with actual experimental practice. We present examples of almost repeatable measurements of continuous observables and some realistic models of weakly disturbing measurements. PACS no.: 03.65.Bz FOUNDATIONS OF PHYSICS 25 (1995) 1239-1266, DOI: 10.1007/BF02055331 1 Dedicated to Peter Mittelstaedt on the occasion of his 65th birthday. 2 Leaving the Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany. Forthcoming address: Department of Applied Mathematics, University of Hull, Hull HU6 7RX, UK. Address as of 2012: Department of Mathematics, University of York, paul.busch@ york.ac.uk.