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.)
Best Answer
A few days ago a paper was uploaded to the arXiv which answers this question:
"On the connection between the Hilger and Radon--Nikodym derivatives" by Jonathan Eckhardt and Gerald Teschl
http://arxiv.org/abs/1102.2511