In this note, we define a $q$-analogue of the Mahler measures by using the Jackson integral which we call the Jackson $q$-Mahler measures. Especially we study their classical limit for polynomials of one variable.
"Jackson q-Mahler measures." Funct. Approx. Comment. Math. 42 (1) 51 - 58, March 2010. https://doi.org/10.7169/facm/1269437068