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Let I = (0, ∞) with the usual topology and product as max multiplication. Then I becomes a locally compact topological semigroup. Let X be a Banach Space. Let L 1 (I, X) be the Banach space of X-valued measurable functions f such thatIt turns out that f * g ∈ L 1 (I, X) and L 1 (I, X) becomes an L 1 (I)-Banach module. A bounded linear operator T on L 1 (I, X) is called a multiplier of L 1 (I, X) if T (f * g) = f * T g for all f ∈ L 1 (I) and g ∈ L 1 (I, X). We characterize the multipliers of L 1 (I, X) in terms of operator valued measures with point-wise finite variation and give an easy proof of some results of Tewari [12].