# notation meaning - braces in the variable's subscript

I am trying to understand the meaning of the braces in the subscript of a variable. I've encountered it in a paper Distributional Reinforcement Learning with Quantile Regression, page 5

Does it mean "as long as the condition is met"? But what is then the alternative expression, when the condition is not met? Have a look at equation (12):

Do I read the equation 12 correctly:

• the $\theta_i$ becomes equal to its current value plus ( $\tau_i$ minus $\delta$ in cases where $r + \gamma z'$ is less than the current $\theta_i$ ), scaled by $\alpha$

Or do these { } braces have another interpretation? Are they used to denote a piece-wise function?

• They introduce the notation at the end of page 3 in the paper. They say "$\delta_{z}$ denotes a Dirac at $z\in\mathbb{R}$". Did you see that? The same notation with braces seems to indicate the same thing for a set of points instead of a single point. – Jackozee Hakkiuz Jun 25 '18 at 3:52
• Thank you, I am pretty sure that's was the right answer. I had an additional discussion with peers and expression seems to mean "1 when {condition is true}, 0 otherwise" – Kari Jun 26 '18 at 13:58