Let $S = \left\{ \omega _ { 1 } , \omega _ { 2 } , \ldots \right\}$ be the sample space of some experiment. Let $m : S \rightarrow \mathbb { R }$ be given by $\operatorname { m } \left( \omega _ { n } \right) = \frac { 1 } { 3 ^ { n } }$ . Can we define a probability distribution on P so S that $P \left( \left\{ \omega _ { n } \right\} \right) = m \left( \omega _ { n } \right)$

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The Answer of Let $S = \left\{ \omega _ { 1 } , \omega _ { 2 } , \ldots \right\}$ be the sample space of some experiment. Let $m : S \rightarrow \mathbb { R }$ be given by $\operatorname { m } \left( \omega _ { n } \right) = \frac { 1 } { 3 ^ { n } }$ . Can we define a probability distribution on P so S that $P \left( \left\{ \omega _ { n } \right\} \right) = m \left( \omega _ { n } \right)$

Let S={ω1,ω2,…}S = \left\{ \omega _ { 1 } , \omega _ { 2 } , \ldots \right\}S={ω1​,ω2​,…}

Let $S = \left\{ \omega _ { 1 } , \omega _ { 2 } , \ldots \right\}$