Difference between revisions of "Regulated"
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| − | 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 [[ | + | 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. |
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| + | =Properties= | ||
| + | [[Rd-continuous implies regulated]]<br /> | ||
=References= | =References= | ||
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=findme|next=Rd-continuous}}: Definition $1.57$ | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=findme|next=Rd-continuous}}: Definition $1.57$ | ||
| + | * {{PaperReference|Functional series on time scales|2008|Dorota Mozyrska|author2=Ewa Pawluszewicz|prev=Delta derivative|next=rd-continuous}} | ||
Latest revision as of 14:50, 21 October 2017
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)
