How do the following r.v. notations read in plain English?

Question

^{Source: Schaum's Outline of Theory and Problems of Probability, Random Variables, and Random Processes. Page-122}

How do the following notations read in plain English?

• $(Y\le y)=[g(X)\le y]=(X \in D_Y)$
• $F_Y(y)=P(Y\le y)=P[g(X) \le y] = P(X \in D_Y)$
• $\displaystyle F_Y(y)=\int_{D_Y} f_X(x)\, dx$