Definition 13.12.6F7490AE48EAC

Definition 13.12.6.F7490AE48EAC Let $U$ be an open subset of $X$. Let $(f_ i)_{i\in I}$ be a net of Borel measurable functions $f_ i\colon U\rightarrow [-\infty ,\infty ]$, and $f\colon U\rightarrow [-\infty ,\infty ]$ be a Borel measurable function. We say $(f_ i)_{i\in I}$ converges to $f$ in capacity if for any $\delta >0$, we have

We sometimes write $f_ i\xrightarrow {\mathrm{C}} f$.