a question about the `standard_normal_logprob` function

[Nicolas Gong]

Hi,
I'm confused about the formula below:

I can understand the calculation of entropy by the formula below,

However, I cannot understand why the first item is calculated by standard_normal_logprob function, the function looks like a sum of lnf(x). how this function can correspond to the first item?

Thank you

[Nicolas Gong]

Monte Carlo Methods