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This paper concerns the problems of the measurability and measurement of random time-variant linear channels. With regard to measurability, a new, less stringent channel measurability criterion is proposed to supersede the BL product introduced by Kailath. This criterion involves the area of occupancy of the Doppler-delay spread function (or its dual). By using time and bandwidth constraints on the input and output of a channel, channel measurement is reduced to the measurement of a discrete set of finite parameters. Optimal measurement techniques are described and their performances determined for both known and unknown channel correlation functions.