I was given the following definition:

Then this example:

It is said that $\mathbb P_1\ll\mathbb P_2$ , but I don't really see it.Please help.
I was given the following definition:

Then this example:

It is said that $\mathbb P_1\ll\mathbb P_2$ , but I don't really see it.Please help.
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$\mathbb{P}_{2}$ is only $0$ on the empty set but $\mathbb{P}_{1}$ also satisfies this.