ABSTRACT
In this paper, we introduce the concept of -measurability and establish the combined measure theory on time scales. Particularly, one can obtain Δ-measure theory and ∇-measure theory on time scales by letting
and
, respectively. Moreover, some criteria for
-measurability of a set are obtained and the notion of Lebesgue
-measurable functions is introduced and studied. Based on it, the Lebesgue
-integral and Riemann
-integral are introduced and the relation between them is discussed.
Disclosure statement
The authors declare that they have no competing interests.