Math notation: What does $I$ mean in this context?

Question

Sorry if this is a noobish question, but I don't know what $I$ means in this context:

$$\hat{f}(X) = \sum_{m=1}^5 c_m I\{(X_1, X_2) \in R_m\}$$

I am reading about Decision Trees in The Elements of Statistical Learning.¹ $I$ isn't introduced² so I assume it is a kind of operator on the following set?

Thanks a lot for any explanation!

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¹ T. Hastie, R. Tibshirani, J. Friedman: The Elements of Statistical Learning, second edition, Springer 2009, p. 305.

² I haven't worked through the whole book, but at least it isn't introduced in this chapter and there is no general section about notation as far as I see.

Answer 1

It most likely means the function that is one when the statement within the curly brackets is true, and zero otherwise. i.e. The function $f$ defined by $$f(X_1, X_2) = I\{(X_1, X_2) \in R_m\}$$ equals $1$ if $(X_1, X_2) \in R_m$, and equals $0$ otherwise. It is called an indicator function.