We study certain algebraic projections on measure algebra (of a locally compact abelian group) which extends to bounded projections on the uniform closure of the Fourier-Modified-Stieltjes transforms. These projections arise by studying a Raikov system of subsets induced by locally compact subgroups. These results generalize the inequality (where μ is measure algebra, μ d is discrete part of μ and is the sup-norm of the Fourier-Modified-Stieltjes transforms.)