Im reading a paper. In this text introduce a condition very similar to the definition of a fuction be lipschitz.
$A$ is a compact space, $m\in\mathbb{P}(S)$ ($\mathbb{P}(S)$ space of probabilities of $s$ components, example $m\in\mathbb{P}(3), m=(1/4,1/4,2/4)$), $L_r>0$ a constant.
$||m-m'||_{\infty}=\max{\{|m_1-m_1'|,...,|m_s-m_s'|\}}$
Looking for fuctions than maybe satisfies this condition.
I already try using combinations of functions with the form
$r(m,a)=g(a)(m_1+...+m_s)$
and $g(a)$ be exponential, and log, but with no success.