where f ∈ L1(μ∗ν), μ,ν ∈ M(S) and τ(x,y) = xy, x,y ∈ S for a locally compact
group S to locally compact semigroups with separately continuous multiplication.
More precisely, we show that for such semigroups, the same convolution formula is
valid if the measure μ × ν is replaced by a suitable measure on S × S (closely
related to μ × ν), thus improving a result of I. Glickberg and complementing
results of B. E. Johnson. Some important consequences of this convolution
formula in abstract harmonic analysis on separately continuous semigroups are
discussed.
