Time-scale Calculus - Measure Theory On Time Scales

Measure Theory On Time Scales

Associated with every time scale is a natural measure defined via

where denotes Lebesgue measure and is the backward shift operator defined on . The delta integral turns out to be the usual Lebesgue–Stieltjes integral with respect to this measure

and the delta derivative turns out to be the Radon–Nikodym derivative with respect to this measure

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