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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
12
votes
Accepted
Associative mean
Yes there are more such functions, even if we require them to be symmetric, monotonic and continuous. For example pick any $C$ and take
$m_C(a,b)=\min(a,b)$ if $a,b\ge C$,
$m_C(a,b)=\max(a,b)$ if $a …