Difference between revisions of "Rd-continuous"
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| − | 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 [[dense point|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. | + | 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 [[dense point|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 derivative|delta differentiable]] by the notation $C_{\mathrm{rd}}^n(\mathbb{T},X)$. |
Revision as of 03:59, 19 February 2016
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 $C_{\mathrm{rd}}^n(\mathbb{T},X)$.
