Definition (Measure) A measure on a σ-algebra A on a set X is mapping μ:A→[0,∞] such that μ(∅)=0, for every sequence (An)n∈N of pairwise disjoint sets An∈A μ(n=1⋃∞An)=n=1∑∞μ(An).
Definition (Measure)
A measure on a σ-algebra A on a set X is mapping μ:A→[0,∞] such that
for every sequence (An)n∈N of pairwise disjoint sets An∈A
Definition (Measure Space) A measure space is a triple (X,A,μ) of a set X, a σ-algebra A on X and a measure μ on A.
Definition (Measure Space)
A measure space is a triple (X,A,μ) of a set X, a σ-algebra A on X and a measure μ on A.