I'm reading the textbook Stochastic Calculus for Finance: Volume I by Steven Shreve, and on page 101 (in case somebody has it on hand) I am unsure of the notation.
There is an "I" where the top and bottom horizontal lines are connected by two vertical lines, instead of just one: $\mathbb{I}$. There is then a subscript saying {τ<=N}, denoting that this mystery operator applies to all tau less than or equal to N.
The "I" looks very similar to the "E", meaning expectation and "P" meaning probability measure, in that there is a duplication of vertical lines to make the letter look hollow.
What is this mystery operator?
I what you are asking about in fact is an indicator function. Consider a set $A\subset \mathbb{R}^n$, then the indicator function for the set $A$ as a function of $x\in\mathbb{R}^n$, is defined as
$$ \mathbb{1}_{A}\left(x\right) := \begin{cases} 1,\qquad \forall x\in A,\\ 0,\qquad \forall x\not\in A. \end{cases} $$
This is very useful in many areas of mathematics, and not least within stochastic calculus which is used in financial mathematics.