Periodic Delta Function and Poisson Integral for - Gauge-institute.org

Gauge Institute JournalH. Vic Dannonby its lowest value on each interval3.2∑x∈[ a, b]⎛⎜⎝dx dx2 2[ x − , x + ]⎞inf f ( t)dx⎠⎟x− ≤t≤ x+dx dx2 2The Upper Integral is the Integration Sum where f ( x ) is replacedby its largest value on each interval3.3∑x∈[ a, b]⎛⎜⎝dx dx2 2[ x − , x + ]⎞ sup f ( t)dx⎠⎟x− ≤t≤ x+dx dx2 2If the integral is a finite hyper-real, we have3.4 A hyper-real function has a finite integral if and only if itsupper integral and its lower integral are finite, and differ by aninfinitesimal.18