# What does the notation $\mathcal{N}(z; \mu, \sigma)$ stand for in statistics?

I know that the notation $$\mathcal{N}(\mu, \sigma)$$ stands for a normal distribution. But I'm reading the book "An Introduction to Variational Autoencoders" and in it, there is this notation: $$\mathcal{N}(z; 0, I)$$ What does it mean?

picture of the book:

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– nbro
Jan 10 at 15:54

It means that $$z$$ has a (multivariate) normal distribution with 0 mean and identity covariance matrix. This essentially means each individual element of the vector $$z$$ has a standard normal distribution.