Let E ( · ) denote the expectation of a random variable. We bound from above our probability of interest by a sum of three probabilities as follows. where the last inequality follows from {| $^{∑}$$_{I}$( − ˆ H I UV + E ( ˆ H I $_{UV}$)) | + | $^{∑}$$_{I}$( − E ( ˆ H I $_{UV}$) + H I $_{UV}$) | + | $^{∑}$$_{I}$( − H I UV + H I U + H I V + H$_{UV}$ ) | > | Π | ϵ } ⊆ { ( | $^{∑}$$_{I}$( − ˆ H I UV + E ( ˆ H I $_{UV}$)) | > | Π | ϵ/ 3) ∪ ( | $^{∑}$$_{I}$( − E ( ˆ H I $_{UV}$) + H I $_{UV}$) | > | Π | ϵ/ 3) ∪ | $^{∑}$$_{I}$( − H I UV + H I U + H I V + H$_{UV}$ ) | > | Π | ϵ/ 3 } and Bonferroni’s inequality. We will show that the three probabilities (B.6)–(B.8) vanish as N → ∞ ,m → ∞ , m √ N → 0, thus proving the theorem. 56 + Pr ( | ∑ I ( − H I UV + H I U + H I V + H$_{UV}$ ) | > | Π | ϵ/ 3) , (B.8) + Pr ( | ∑ I ( − E ( ˆ H I $_{UV}$) + H I $_{UV}$) | > | Π | ϵ/ 3) (B.7) Pr$^{(}$$^{∣}$ ∣ ∣ S ADP m × m N | Π | − I$_{XY}$$^{∣}$ ∣ ∣ > ϵ$^{)}$ = Pr$^{(}$$^{∣}$ ∣ ∣ $^{∑}$$_{I}$T I m × $_{m}$( L ) N | Π | − I$_{XY}$$^{∣}$ ∣ ∣ > ϵ$^{)}$ = Pr$^{(}$$^{∣}$ ∣ ∣ $^{∑}$$_{I}$( H I U + H I V − ˆ H I $_{UV}$) | Π | + H$_{UV}$$^{∣}$ ∣ ∣ > ϵ$^{)}$ = Pr ( | ∑ I ( H I U + H I V − ˆ H I UV + H$_{UV}$ ) | > | Π | ϵ ) = Pr ( | ∑ I ( − ˆ H I UV + E ( ˆ H I $_{UV}$)) + ∑ I ( − E ( ˆ H I $_{UV}$) + H I $_{UV}$) + ∑ I ( − H I UV + H I U + H I V + H$_{UV}$ ) | > | Π | ϵ ) ≤ Pr ( | ∑ I ( − ˆ H I UV + E ( ˆ H I $_{UV}$)) | + | ∑ I ( − E ( ˆ H I $_{UV}$) + H I $_{UV}$) | + | ∑ I ( − H I UV + H I U + H I V + H$_{UV}$ ) | > | Π | ϵ ) ≤ Pr ( | ∑ I ( − ˆ H I UV + E ( ˆ H I $_{UV}$)) | > | Π | ϵ/ 3) (B.6)