Difference between revisions of "Nabla derivative at left-scattered"
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(Created page with "==Theorem== If $f$ is continuous at $t$ and $t$ is left-scattered, then $$f^{\nabla}(t) = \dfrac{f(t)-f(\rho(t))}{\nu(t)}.$$ ==Proof== ==References== ...") |
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==Theorem== | ==Theorem== | ||
| − | If $f$ is continuous at $t$ and $t$ is [[scattered point|left-scattered]], then | + | If $f$ is [[continuity|continuous]] at $t$ and $t$ is [[scattered point|left-scattered]], then |
| − | $$f^{\nabla}(t) = \dfrac{f(t)-f(\rho(t))}{\nu(t)} | + | $$f^{\nabla}(t) = \dfrac{f(t)-f(\rho(t))}{\nu(t)},$$ |
| + | where $f^{\nabla}$ denotes the [[nabla derivative]], $\rho$ denotes the [[backward jump]], and $\nu$ denotes the [[backward graininess]]. | ||
==Proof== | ==Proof== | ||
Latest revision as of 00:58, 23 August 2016
Theorem
If $f$ is continuous at $t$ and $t$ is left-scattered, then $$f^{\nabla}(t) = \dfrac{f(t)-f(\rho(t))}{\nu(t)},$$ where $f^{\nabla}$ denotes the nabla derivative, $\rho$ denotes the backward jump, and $\nu$ denotes the backward graininess.
