3 problems

Both-types invariance conjecture. The only such pairs are the quasi-arithmetic transforms

Let $X_1,X_2,\ldots$ be independent observations from the Cauchy model, with parameter $\theta$, and let $f$ be a generator of a quasi-arithmetic mean satisfying the residue and ex…

Local Hardy characterization conjecture. The quasi-arithmetic mean $\mathscr{A}^{[f]}$ has the weak-Hardy property if and only if there exists $\varepsilon\in I$ such that…