# Difference between revisions of "Delta integral from t to sigma(t)"

From timescalewiki

Line 2: | Line 2: | ||

The following formula holds: | The following formula holds: | ||

$$\int_t^{\sigma(t)} f(\tau) \Delta \tau = \mu(t)f(t),$$ | $$\int_t^{\sigma(t)} f(\tau) \Delta \tau = \mu(t)f(t),$$ | ||

− | where $\int$ denotes the [[delta integral]] and $\mu$ denotes the [[forward graininess]]. | + | where $\int$ denotes the [[delta integral]], $\sigma$ denotes the [[forward jump]], and $\mu$ denotes the [[forward graininess]]. |

==Proof== | ==Proof== |

## Revision as of 22:39, 22 August 2016

## Theorem

The following formula holds: $$\int_t^{\sigma(t)} f(\tau) \Delta \tau = \mu(t)f(t),$$ where $\int$ denotes the delta integral, $\sigma$ denotes the forward jump, and $\mu$ denotes the forward graininess.