Professor Brown is widely known for his contributions to measure theory and in particular for his work on the structure of convolution measure algebras. He was one of the first to recognise the importance of measure algebras for harmonic analysis and probability theory and in a series of deep going papers written mostly in association with W. Moran, he clarified significantly their algebraic structure.
Perhaps his most significant individual achievement so far is a complete description of the structure of Reisz product measure which arise from a famous classical example due to F. Riesz. Here Brown's originality and craftsmanship show up in full. For years mathematicians were laboriously constructing examples of measures with particular structural properties. Such examples can now be manufactured at will from specific Riesz products, due to Brown's structure theorems.
In recognition of his distinguished contributions to measure theory Professor Brown was awarded the Sir Edmund Whittaker prize of the Edinburgh Royal Society in 1977.