Let $P$ and $Q$ be probability measures on a measurable space $(X, \mathcal{X})$. Then, we say that $P$ is dominated by (or absolutely continuous with respect to) $Q$, in symbols $Q \, \triangleright \, P$, if for all $B \in \mathcal{X}$ we have that if $Q(B)=0$, then also $P(B)=0$.
Now, let $K$ be a compact subset of $\mathbb{R}^d$, $d \in \mathbb{N}$. Let $\{Q_t,t \in K\}$ be a class of probability measures on $(X, \mathcal{X})$. Does the formula $$ \textbf{(1)} \hspace{5em} Q(B):=\sup_{t\in K}Q_t(B), \quad B \in \mathcal{X}, $$
define a probability measure? If not, is there any notion similar to domination of $P$ by an object $Q$ defined as in $\textbf{(1)}$?