Confused about HSI and HSL color spaces
L(x,y) here is a function for luma, a non-linear approximation of luminance. As you can see, it's the weighted sum of the R'G'B' values. The prime symbol (') indicates that they have been gamma-corrected for perceptual uniformity. The coefficients used in this case are standardized by ITU-R Recommendation BT.601. Other standards, such as BT.709 (which may be preferred for its higher accuracy), exist as well.

See: http://en.wikipedia.org/wiki/HSL_and_HSV#Lightness. I can't answer whether you can use luma and still say that it's a component of HSL or HSI. If the author of the book gave you that formula, I suspect you can assume so, at least for that text.