About the same time, it seems, as I asked this question, a new post appeared on the wikipedia discussion page for Time scale calculus which suggests the Time scale derivative (aka Hilger derivative aka delta-derivative) is the same as the Radon-Nikodym derivative of the Lebesgue–Stieltjes integral.

Do you agree that the time scale delta-derivative is a Lebesgue–Stieltjes derivative with the appropriate weight function? (The notion of Lebesgue–Stieltjes derivative being similarly defined to the Riemann-Stieltjes derivative of my previous question.)