Previously, a coding theorem and its converse for stationary asymptotically memoryless continuous-time channels were proved, giving the capacity

with an almost sure constraint on the input cost. For calculation, it is more convenient to find a capacity

with the constraint on the expected input cost. Obviously,

, but the coding theorem may not hold for

. For a class of input costs typified by the time-average power, we prove the coding theorem for

by directly showing

.