The equivalence Vitali cover integral with Lebesgue integral

Collection interval v is called Vitali Cover measiu’able set up A ⊂ R, if for every number ε > 0 and x ∈ A is an open interval I x ∈ v so that x ∈ I x and μ( I x ) < ε. By utilizing Vitali Cover can be constructed of a type of integral type, hereinafter referred Riemaim Vitali Cover integral. A Function f : [ a , b ] → R ¯ A function is said to Lebesgue integrable if and only if there is a continuous function F : [ a , b ] → R ¯ so that F absolutely continuous on [ a,b ] and F ′( x ) = f(x) almost everywhere in [ a,b ]. By using the properties of Vitali Cover can be shown that both types of the above integral are equivalent