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Arithmetic coding, the termination symbol, and the empty string

Strings consisting of a bunch of $b$'s and $c$'s ending with an $a$ (the termination symbol) are valid for encoding. Strings with an $a$ in middle are considered invalid for encoding. … But does arithmetic coding assign any string an encoding in the interval $[0, P(a))$? Would the empty string qualify as being encoded to a bitstring lying in $[0, P(a))$? …