Anemometer beam exits reflect, or backscatter, the light back into a detector, where it is measured relative to the original laser beam. When the particles are in great motion, they produce a Doppler shift for measuring wind speed in the laser light, which is used to calculate the speed of the particles, and therefore the air around the anemometer. Ultrasonic anemometers, first developed in the 1950s, use ultrasonic sound waves to measure wind velocity. They measure wind speed based on the time of flight of sonic pulses between pairs of transducers. Measurements from pairs of transducers can be combined to yield
Signed measure finite signed measure is given by for all "A" in Σ. This signed measure takes only finite values. To allow it to take +∞ as a value, one needs to replace the assumption about "f" being absolutely integrable with the more relaxed condition where "f"("x") = max(−"f"("x"), 0) is the negative part of "f". What follows are two results which will imply that an extended signed measure is the difference of two nonnegative measures, and a finite signed measure is the difference of two finite non-negative measures. The Hahn decomposition theorem states that given a signed measure μ, there exist