# Difference between revisions of "Pre-differentiable"

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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 pre-differentiable with region of differentiation $D \subset \mathbb{T}^{\kappa}$ if $f$ id [[delta derivative|delta differentiable]] at all $t \in D$ and $\mathbb{T}^{\kappa} \setminus D$ is countable and contains no [[scattered point|right-scattered]] points in $\mathbb{T}$. | Let $\mathbb{T}$ be a [[time scale]] and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. We say that $f$ is pre-differentiable with region of differentiation $D \subset \mathbb{T}^{\kappa}$ if $f$ id [[delta derivative|delta differentiable]] at all $t \in D$ and $\mathbb{T}^{\kappa} \setminus D$ is countable and contains no [[scattered point|right-scattered]] points in $\mathbb{T}$. | ||

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+ | =References= | ||

+ | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=findme|next=findme}}: Definition $1.62$ |

## Revision as of 23:41, 4 January 2017

Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. We say that $f$ is pre-differentiable with region of differentiation $D \subset \mathbb{T}^{\kappa}$ if $f$ id delta differentiable at all $t \in D$ and $\mathbb{T}^{\kappa} \setminus D$ is countable and contains no right-scattered points in $\mathbb{T}$.

# References

- Martin Bohner and Allan Peterson:
*Dynamic Equations on Time Scales*(2001)... (previous)... (next): Definition $1.62$