Quotation "Premultiplied vs. Un-Premultiplied Color Channels"

quote from Technical Introduction to OpenEXR.

Premultiplied vs. Un-Premultiplied Color Channels
The A, AR, AG, and AB channels in an OpenEXR image represent alpha or opacity: 0.0 means the pixel is
transparent; 1.0 means the pixel is opaque. By convention, all color channels are premultiplied by alpha,
so that
composite = foreground + (1-alpha) × background

performs a correct "over" operation.
Describing the color channels as "premultiplied" is a shorthand for describing a correct "over" operation.
With un-premultiplied color channels "over" operations would require computing
composite = alpha × foreground + (1-alpha) × background

"Premultiplied" does not mean that pixels with zero alpha and non-zero color channels are illegal. Such a
pixel represents an object that emits light even though it is completely transparent, for example, a candle
flame.