As we saw in §§5 and 6, this premeasure induces an outer measure m∗ on all subsets of En; and m∗, in turn, induces a measure m on the σ-field M∗ of \...As we saw in §§5 and 6, this premeasure induces an outer measure m∗ on all subsets of En; and m∗, in turn, induces a measure m on the σ-field M∗ of m∗-measurable sets. More generally, a σ-finite set A∈M in a measure space (S,M,μ) is a countable union of disjoint sets of finite measure (Corollary 1 of §1).
As we saw in §§5 and 6, this premeasure induces an outer measure m∗ on all subsets of En; and m∗, in turn, induces a measure m on the σ-field M∗ of \...As we saw in §§5 and 6, this premeasure induces an outer measure m∗ on all subsets of En; and m∗, in turn, induces a measure m on the σ-field M∗ of m∗-measurable sets. More generally, a σ-finite set A∈M in a measure space (S,M,μ) is a countable union of disjoint sets of finite measure (Corollary 1 of §1).
