I'm reading a probability textbook on stochastic processes (Jochen Wengenroth's "Wahrscheinlichkeitstheorie", de Gruyter 2008) and the following notation: "$\mathcal{F}_\tau^+$" came up in the statement of one of the theorems, without this notation having been defined previously in the book. If this is a standard notation, I'd appreciate it if someone could give me a formal definition of it. If it's not a standard notation, and someone has a guess as to what it might mean, please let me know. Thanks.
Here is the statement of the theorem featuring this notation (translated from German, p. 144).
Theorem 7.14 (Strong Lévy property) Let $X = (X_t)_{t \geq 0}$ be a Lévy process adapted to the filtration $\mathcal{F}$ and let $\tau$ be a real-valued $\mathcal{F}$ stopping time. Then the following process $Y_t \equiv X_{\tau + t} - X_\tau$ is independent of $\mathcal{F}_\tau^+$ and satisfies $Y \overset{d}{=} X$.
And here is the definition of a similar notation defined previously in the same chapter (p. 142).
Given a filtration $\mathcal{F} = (\mathcal{F}_t)_{t \geq 0}$, the right-continuous filtration $\mathcal{F}^+$ is defined as follows: $\mathcal{F}^+_t \equiv \bigcap_{s > t} \mathcal{F}_s$.
Wengenroth uses the more explicit version of $\mathcal F_\tau^+$ in the paragraph preceding theorem 7.12 on page 142, namely $(\mathcal F^+)_\tau$. $\mathcal F_\tau^+$ is the $\sigma$-algebra of $\mathcal F^+$ events before $\tau$, that is