Anemometer turbines usually requires a refresh rate of wind speed measurements of 3 Hz, easily achieved by sonic anemometers. Three-dimensional sonic anemometers are widely used to measure gas emissions and ecosystem fluxes using the eddy covariance method when used with fast-response infrared gas analyzers or laser-based analyzers. Two-dimensional wind sensors are of two types: Acoustic resonance anemometers are a more recent variant of sonic anemometer. The technology was invented by Dr Savvas Kapartis and patented in 2000. Whereas conventional sonic anemometers rely on time of flight measurement, acoustic resonance sensors use resonating acoustic (ultrasonic) waves within a small purpose-built cavity in
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,