Recent advantages in experimental quantum physics call for a careful r
econsideration of the measurement process ill quantum mechanics. III t
his paper we describe the structure of the ideal measurements and thei
r status among tile repeatable measurements. Then we provide an exhaus
tive account of tile interrelations between repeatability and the appa
rently weaker notions of value reproducible oi first-kind measurements
. We demonstrate the close link between repeatable measurements and di
screte observables and show how the ensuing measurement limitations fo
r continuous observables can be lifted in a way that is ill full accor
dance with actual experimental practice. We present examples of almost
repeatable measurements of continuous observables and some realistic
models of weakly disturbing measurements.