In mathematics, particularly functional analysis, the Dunford–Schwartz theorem, named after Nelson Dunford and Jacob T. Schwartz states that the averages of powers of certain norm-bounded operators on L1 converge in a suitable sense.
Theorem. Let be a linear operator from to with and . Then
exists almost everywhere for all .
The statement is no longer true when the boundedness condition is relaxed to even .
|This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.|