Rd-continuous

Let $\mathbb{T}$ be a time scale and $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be a regulated function. We say that $f$ is rd-continuous if for any right dense point $t \in \mathbb{T}$, $f(t) = \displaystyle\lim_{\xi \rightarrow t^+} f(\xi)$. In other words, $f$ is rd-continuous if it is regulated and continuous at right dense points. The notation $C_{\mathrm{rd}}(\mathbb{T},X)$ denotes the set of rd-continuous functions $g \colon \mathbb{T} \rightarrow X$. We denote the set of rd-continuous functions that are $n$-times delta differentiable by the notation $C_{\mathrm{rd}}^n(\mathbb{T},X)$.

Properties

Continuous implies rd-continuous
rd-continuous implies regulated
Forward jump is rd-continuous

References

• Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Definition $1.58$