Integrands Relating to Formats of Duration

Things that we normally coceive of happen over time, as everyone knows. When something is integrated over time, that means that whatever operation or function that you are refering to is happening over a duration of time. Such as amperage is charge per time, and, power is energy per time. The simple comment that you made (how does one relate to different formats of metrical durations) does, though, bring up an important point.: How would one integrate durations that occur over sub-Fouriers that involve less than the Planck time -- less than a discrete unit of time. For the sake of using a relatively common manner of terminology, one may possibly use, as a suggestion, del-like simbals in order to integrate certain gauge-metrics over a sub-Fourier Transformation in the effort to communicate as to how an operation or a function happens over the given arbitrary duration that here happens in less than a discrete unit of time. So, when one considers a certain general format of gauge-metric-based duration that is relatively large in comparison to a relatively infinitessimal gauge-metric, one may possibally use one format of del-like simbal that may be integrated over the said arbitrary sub-Fourier in order to work to describe the piecewise continuity of the flow of motion in which a given arbitrary phenomenon moves over the here proscribed duration. Yet, depending upon how much smaller the proscribed general duration of any given arbitrary gauge-metric is, one may use a variety of del-simbals in order to work to describe different various piecewise sub-Fourier Transformations so that one may be able to accurately communicate to others the Hamiltonian-based nature of various different flows of motion. The most infinitessimal durations that are briefer than a discrete unit of time would have their own del-like simbal, so, under such considerations, one may apply such an arbitrary method of corelationship in order to describe the general flow of any given arbitrary phenomenon in a piecewise manner over the gauge-metrics that would here bear a tense of virtual static equilibrium over a state of superconformal invariance. I appologize if my manner of communicating is a little bit off or non-conventional, yet, such considerations are important. Perfection is a fallacy. So, a question as to how to express those integrands that inter-relate to different formats of durations does ring out an important point  And I thank you that such a simple question is here able to afford the plausability of being addressed. Sincerely, Samuel David Roach.