We show that many integral convergence theorems are equivalent to the dominated convergence theorem, and that they are strictly weaker than the monotone convergence theorem. The precise sense of these assertions are given.

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# Comparison of the Powers of Convergence Theorems for Integrals

We show that many integral convergence theorems are equivalent to the dominated convergence theorem, and that they are strictly weaker than the monotone convergence theorem. The precise sense of these assertions are given.

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