> In the standard foundations of probability theory, as laid out by Kolmogorov, we can then model these events and random variables by introducing a sample space (which will be a probability space) to capture all the ambient sources of randomness; events are then modeled as measurable subsets of this sample space, and random variables are modeled as measurable functions on this sample space.

This matches the definitions of Wikipedia pretty closely: "A probability space consists of three parts: A sample space [...], A set of events [...], The assignment of probabilities to the events".

So either you misunderstood that sentence or both Wikipedia and Terrence Tao are wrong.