# Regulated

From timescalewiki

Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. We say that $f$ is regulated if for all right dense points $t_1 \in \mathbb{T}$, $\displaystyle\lim_{\xi \rightarrow t_1^+} f(\xi)$ exists and for all left dense points $t_2 \in \mathbb{T}$, $\displaystyle\lim_{\xi \rightarrow t_2^-} f(\xi)$ exists.

# Properties

Rd-continuous implies regulated

# References

- Martin Bohner and Allan Peterson:
*Dynamic Equations on Time Scales*(2001)... (previous)... (next): Definition $1.57$ - Dorota Mozyrska and Ewa Pawluszewicz:
*Functional series on time scales*(2008)... (previous)... (next)