Let $f$ be a function from $[0,1]$ to bounded Borel subsets of some Euclidean space $\mathbb{R}^d$.
Suppose $f$ satisfies the following property: for every $\epsilon>0$ there exists some $\delta>0$ such that
$$|t-t'|<\delta$$
implies
$$\textrm{Lebesgue}(f(t)\ominus f(t'))<\epsilon$$
where $\ominus$ denotes symmetric set difference.
This is a kind of continuity property: when $t$ and $t'$ are sufficiently close, I want $f(t)$ and $f(t')$ to also be similar.
Is there a standard term for this property?