Candela was chosen so that the new definition would precisely match the old definition. Although the candela is now defined in terms of the second (an SI base unit) and the watt (a derived SI unit), the candela remains a base unit of the SI system, by definition. If a source emits a known luminous intensity "I" (in candelas) in a well-defined cone, the total luminous flux "Φ" in lumens is given by where "A" is the "radiation angle" of the lamp—the full vertex angle of the emission cone. For example, a lamp that emits 590 cd with a radiation angle
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