Let A & M and μ*(A) < oo. Then, for each e > 0,there exist B₁, B2,..., Bk C, k<∞o with BinB;=0 for 1 ≤i #j≤k,such thatk4²(AAÙB) <<j=1where for any two sets E₁ and E2, E1 E2 is the symmetric difference ofE₁ and E2, defined by E₁ E2 = (E₁ ^ E²) U (E† E₂).

Suppose A∈Μμ with μ(A)<∞ and let ε>0 be given.By Lebesgue-Stieltjes theorem, we can find an…

Let A & M and μ*(A) < oo. Then, for each e > 0, there exist B₁, B2,..., Bk EC, k<∞o with Bin B₁ = 0 for 1 ≤i #j≤k, such that ~ (AA UB₂) <² €, j=1 where for any two sets E₁ and E2, E1 ▲ E2 is the symmetric difference of E1 and E2, defined by E₁ A E2 = (E₁ E₂) U (E₁ E₂).

Let A & M and μ*(A) < oo. Then, for each e > 0, there exist B₁, B2,..., Bk EC, k<∞o with Bin B₁ = 0 for 1 ≤i #j≤k, such that ~ (AA UB₂) <² €, j=1 where for any two sets E₁ and E2, E1 ▲ E2 is the symmetric difference of E1 and E2, defined by E₁ A E2 = (E₁ E₂) U (E₁ E₂).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 56E

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Question

Let A & M and μ*(A) < oo. Then, for each e > 0,
there exist B₁, B2,..., Bk C, k<∞o with BinB;=0 for 1 ≤i #j≤k,
such that
k
4²(AAÙB) <<
j=1
where for any two sets E₁ and E2, E1 E2 is the symmetric difference of
E₁ and E2, defined by E₁ E2 = (E₁ ^ E²) U (E† E₂).

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