Vol ( N ) {\displaystyle \operatorname {Vol} ({\mathfrak {N}})} ≥ {\displaystyle \,\geq \,} Vol ( X ∪ Y ∪ B ) {\displaystyle \operatorname {Vol} (X\cup Y\cup B)} = {\displaystyle \,=\,} Vol ( ⋃ i ∈ I T i ~ ) + Vol ( B ) {\displaystyle \operatorname {Vol} (\bigcup _{i\in I}{\tilde {T_{i}}})+\operatorname {Vol} (B)} > {\displaystyle \,>\,} ∑ i ∈ I Vol ( T ~ i ) {\displaystyle \sum _{i\in I}\operatorname {Vol} ({\tilde {T}}_{i})} = {\displaystyle \,=\,} ∑ i ∈ I Vol ( T i ) {\displaystyle \sum _{i\in I}\operatorname {Vol} (T_{i})} = {\displaystyle \,=\,} Vol ( T ) {\displaystyle \operatorname {Vol} (T)} ≥ {\displaystyle \,\geq \,} 2 n Vol ( M ) {\displaystyle 2^{n}\operatorname {Vol} ({\mathfrak {M}})} = {\displaystyle \,=\,} Vol ( N ) . {\displaystyle \operatorname {Vol} ({\mathfrak {N}})\,.}
