Apparently the left invariant measure is 1/a^2 dadb, and the right invariant measure is 1/a dadb. The book I have just sticks to left measures, and is an engineering book so it doesn't really get into details that a math book would (the whole group theory chapter is 31 pages out of a 1500 page book and the wavelet portion is ~2 pages, though it also has an 8 page section on wavelets in a previous chapter). It's very much a "what are groups, what are representations, and why do they matter for physics and signal processing" kind of thing. For reference it's Barrett & Myers Foundations of Image Science.