Anemometer constant torque and responded more quickly to gusts than the four-cup anemometer. The three-cup anemometer was further modified by the Australian Dr. Derek Weston in 1991 to measure both wind direction and wind speed. Weston added a tag to one cup, which causes the cupwheel speed to increase and decrease as the tag moves alternately with and against the wind. Wind direction is calculated from these cyclical changes in cupwheel speed, while wind speed is determined from the average cupwheel speed. Three-cup anemometers are currently used as the industry standard for wind resource assessment studies & practice. One of the
Pre-measure is called "σ"-additivity. Thus, what is missing for a pre-measure to be a measure is that it is not necessarily defined on a sigma-algebra (or a sigma-ring). It turns out that pre-measures give rise quite naturally to outer measures, which are defined for all subsets of the space "X". More precisely, if "μ" is a pre-measure defined on a ring of subsets "R" of the space "X", then the set function "μ" defined by is an outer measure on "X" and the measure "μ" induced by "μ" on the σ-algebra Σ of Carathéodory-measurable sets satisfies formula_4 for formula_5 (in particular,