fact: Definition vitali_collection_partition n := [set i | V i /\ r / (2 ^ n.+1)%:R < (radius (B i))%:num <= r / (2 ^ n)%:R].
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule