Candela frequency and that has a radiant intensity in that direction of watt per steradian. The definition describes how to produce a light source that (by definition) emits one candela, but does not specify the luminosity function for weighting radiation at other frequencies. Such a source could then be used to calibrate instruments designed to measure luminous intensity with reference to a specified luminosity function. An appendix to the SI Brochure makes it clear that the luminosity function is not uniquely specified, but must be selected to fully define the candela. The candela is sometimes still called by the old name
Complete measure Naïvely, we would take the "σ"-algebra on R to be "B" ⊗ "B", the smallest "σ"-algebra containing all measurable "rectangles" "A" × "A" for "A" ∈ "B". While this approach does define a measure space, it has a flaw. Since every singleton set has one-dimensional Lebesgue measure zero, for "any" subset "A" of R. However, suppose that "A" is a non-measurable subset of the real line, such as the Vitali set. Then the "λ"-measure of {0} × "A" is not defined, but and this larger set does have "λ"-measure zero. So, this "two-dimensional Lebesgue measure" as just defined is not