What's the true meaning of $(a + b)^\omega$ in regular expression
The notation is standard but it's an omega ($\omega$, the first infinite ordinal; basically, the infinity in "There are infinitely many natural numbers"), not a&nbsp;$w$ (the 23rd letter of the Latin alphabet).

Both as a closure operator applied to languages and as an operator in $\omega$-regular expressions, $^\omega$ is directly analogous to ${}^*$, except it denotes the concatenation of infinitely many things, rather than any finite number of them.