a saw some proofs of Lebesgue regularity and open set G (for E &#x2208;<!-- ∈ --> <mrow class=

lilmoore11p8

lilmoore11p8

Answered question

2022-07-03

a saw some proofs of Lebesgue regularity and open set G (for E L ) such that λ ( G E ) < ε, but how to proof this one: Namely suppose E L is such that for ε > 0 there exist a closed set F E such that λ ( E F ) < ε?

Answer & Explanation

Jayvion Tyler

Jayvion Tyler

Beginner2022-07-04Added 23 answers

E L E c L
Now, given any ϵ > 0 , G open set such that E c G and λ ( G E c ) < ϵ
As, E c G G c E
Then, G c = F is a closed set and
λ ( G E c ) = λ ( E F ) < ϵ

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