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math.FA2011★ 19 cited
Metastable convergence theorems
Jeremy Avigad, Edward Dean, Jason Rute
The dominated convergence theorem implies that if (f_n) is a sequence of functions on a probability space taking values in the interval [0,1], and (f_n) converges pointwise a.e., t…
math.LO2011★ 32 cited
Algorithmic randomness, reverse mathematics, and the dominated convergence theorem
Jeremy Avigad, Edward Dean, Jason Rute
We analyze the pointwise convergence of a sequence of computable elements of L^1(2^omega) in terms of algorithmic randomness. We consider two ways of expressing the dominated conve…