Measure-preservation criteria for 1-Lipschitz functions on Fq[[T]] in terms of the three bases of Carlitz polynomials, digit derivatives, and digit shifts

As a follow-up to our previous work [10], we characterize the measure-preservation of 1-Lipschitz functions on Fq[[T]] in terms of the three well-known bases: Carlitz polynomials, digit derivatives, and digit shifts.