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 [[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.
 
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=
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[[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 $1.57$
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* {{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