Expression of the Lebesgue \(\Delta\)-integral on time scales as a usual Lebesgue integral; application to the calculus of \(\Delta\)-antiderivatives (Q2489110)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Expression of the Lebesgue \(\Delta\)-integral on time scales as a usual Lebesgue integral; application to the calculus of \(\Delta\)-antiderivatives |
scientific article |
Statements
Expression of the Lebesgue \(\Delta\)-integral on time scales as a usual Lebesgue integral; application to the calculus of \(\Delta\)-antiderivatives (English)
0 references
16 May 2006
0 references
The authors are concerned with the calculation of the Lebesgue \(\Delta\)-integral on time scales. A formula for calculating the Lebesgue \(\Delta\)-integral as a sum of suitable Lebesgue integrals is given. This formula points out the division of the time scales calculus between the ``continuous'' and the ``discrete'' points. By using the relationship between these kind of integrals and the Riemann ones, the given expression is rewritten to obtain the \(\Delta\)-antiderivatives of functions defined on time scales. The obtained results are illustrated by some examples.
0 references
Dynamic equations on time scales
0 references
\(\Delta\)-measure
0 references
\(\Delta\)-antiderivatives
0 references
measure chains
0 references
Lebesgue \(\Delta\)-integral
0 references
0 references
