Anemometer mounted on a vertical shaft. The air flow past the cups in any horizontal direction turned the shaft at a rate that was roughly proportional to the wind speed. Therefore, counting the turns of the shaft over a set time interval produced a value proportional to the average wind speed for a wide range of speeds. It is also called a rotational anemometer. On an anemometer with four cups, it is easy to see that since the cups are arranged symmetrically on the end of the arms, the wind always has the hollow of one cup presented to it and
Haar measure nontrivial but the modular function of formula_3 is trivial. The quotient of these cannot be extended to any character of formula_3, so the quotient space formula_114 (which can be thought of as 1-dimensional real projective space) does not have even a semi-invariant measure. Using the general theory of Lebesgue integration, one can then define an integral for all Borel measurable functions formula_84 on formula_3. This integral is called the Haar integral. If formula_11 is a left Haar measure, then for any Haar integrable function formula_84 on formula_3. This is immediate for indicator functions, being essentially the definition of left invariance.