Say a continuous random variable $X \sim \mathbb{R}$ has a probability density function (p.d.f.).

Is it correct that,

change the probability measure $\Rightarrow$ define a new p.d.f. for X

?

In other words, is „changing the probability measure“ just a fancy way of saying „now assume that $X$ is distributed according to another p.d.f.?

Say a continuous random variable $X \in \mathbb{R}$ has a probability density function (p.d.f.).

Is it correct that,

change the probability measure $\Rightarrow$ define a new p.d.f. for X

?

In other words, is „changing the probability measure“ just a fancy way of saying „now assume that $X$ is distributed according to another p.d.f.?