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I am curious if the Bockstein spectral sequence can detect multiple summands of the same power? E.g two summands $\mathbb{Z}/2\oplus\mathbb{Z}/2$ in the integral homology. Presence of the differential only detects one copy, if I understand correctly? Thanks.
I just realized a problem: We need $|f(x)|^p\ln|f(x)|\leq g(x)$ for all $p$ in order for the "dominating" to work. I think my previous argument on boundedness of $|f(x)|^p\ln|f(x)|$ does not apply, we need boundedness as $p$ varies not as $x$ varies.
