summable function
A measurable function
f:Ω→ℝ where (Ω,𝒜,μ) is a measure space
is said to be summable if the Lebesgue integral
of the absolute value
of f exists and is finite,
| ∫Ω|f|𝑑μ<+∞ |
An alternative way of expressing this condition is to assert that f∈L1(Ω).
Note that some authors distinguish between integrable and summable: an integrable function is one for which the above integral exists; a summable function is one for which the integral exists and is finite.
| Title | summable function |
|---|---|
| Canonical name | SummableFunction |
| Date of creation | 2013-03-22 18:12:14 |
| Last modified on | 2013-03-22 18:12:14 |
| Owner | ehremo (15714) |
| Last modified by | ehremo (15714) |
| Numerical id | 8 |
| Author | ehremo (15714) |
| Entry type | Definition |
| Classification | msc 28A25 |
| Related topic | LebesgueIntegrable |