Dunford–Schwartz theorem
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.
Statement
Let be a linear operator from to with and. Thenexists almost everywhere for all.
The statement is no longer true when the boundedness condition is relaxed to even.