Department of Mathematics2024-11-0920070039-322310.4064/sm182-3-12-s2.0-36649014014http://dx.doi.org/10.4064/sm182-3-1https://hdl.handle.net/20.500.14288/9389Let G be a locally compact abelian group and M(G) its measure algebra. Two measures mu and lambda are said to be equivalent if there exists an invertible measure pi such that pi * mu = lambda. The main result of this note is the following: A measure mu is invertible iff vertical bar(mu) over cap vertical bar >= epsilon on (G) over cap for some epsilon > 0 and mu is equivalent to a measure lambda of the form lambda = a + theta, where a is an element of L-1(G) and theta is an element of M(G) is an idempotent measure.MathematicsJournal Article252417500001Q28787