Unconditional Integrability with Application to Ergodic Theorem
Mangatiana A. Robdera *
Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana.
Dintle N. Kagiso
Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana.
*Author to whom correspondence should be addressed.
Abstract
We present a straightforward introduction to the unconditional integrability in the extended sense. We state and proof useful necessary and sufficient conditions for unconditional integrability of complex or real valued functions. As an application, we obtain a simpler direct proof of mildly extended version of the Birkhoff’s pointwise ergodic theorem.
Keywords: Conditional integrability, conditional expectation, ergodic theorem, pointwise convergence.