Measure Theory

Welcome to Questions LLC's Measure Theory category, where you will find a wealth of knowledge and resources on this fascinating field of mathematics. Measure Theory deals with the mathematical concept of measuring and assigning values to sets, enabling the understanding and analysis of complex structures and phenomena. Whether you are a student, researcher, or simply curious about the intricacies of this subject, our community of experts is here to provide comprehensive answers to your questions. Dive into our extensive collection of Measure Theory questions and enrich your understanding of this fundamental branch of mathematics.

Questions (13)

Show that E is measurable if and only if kE is measurable.
1. 2 answers
2. asked by .
3. 96 views
Let(X,Θ,µ) be a measure space,f a nonnegative measurable function on X.Show that Xfdµ=0 if and only if f=0 µ a.e. on X.
1. 2 answers
2. asked by .
3. 109 views
Let(X,Θ,µ)be a measure space,f be a nonnegative measurable function onX,and ν(E)= Efdµ.Show that ν is a measure.
1. 2 answers
2. asked by .
3. 83 views
Let (X,Θ,µ) be a measure space, and suppose X = n∈Z+ En, where {En} is a pairwise disjoint collection of measurable subsets
1. 2 answers
2. asked by .
3. 124 views
Let (X,@) be a measurable space.Statement 1: it is given that for each a in R the set {x in X | f(x) <= a } is measurable
1. 4 answers
2. asked by .
3. 162 views
Question:Let (X,@) be a measurable space. Prove that if for each a in R, {x in X | f(x) <= a } is measurable, then f is
1. 2 answers
2. asked by .
3. 109 views
How do we find the Lebsgue outer measure of below setSet :
1. 2 answers
2. asked by .
3. 110 views
Let A be a countable subset of R. Show that m∗(A) = 0.
1. 2 answers
2. asked anonymously
3. 74 views
Let {rn} be an enumeration of Q ∩ [0,1] and let > 0. Let B = [0,1] \ A, where A= n=1 (b) Let A =1 2n,rn + 2n. Find the
1. 2 answers
2. asked by .
3. 74 views
Question:For a subset E of R and a number a ∈ R, let a+E = {a+e | e ∈ E}. Show that E is measurable if and only if a+E is
1. 2 answers
2. asked by Need Help of a Human Teacher
3. 98 views
Let A,B ⊆ R. Show that |m∗(A) − m∗(B)| ≤ m∗(A B), where m∗(A B) = (A\B)∪(B\A)
1. 2 answers
2. asked anonymously
3. 58 views
Question:Let A ⊆R such that m∗(A) = 0. Show that if A ∪ B ∈ L, then B ∈ L. My approach: We can write B as B = (A ∪
1. 2 answers
2. asked anonymously
3. 86 views
Question:If m*(E) = 0, show that E is Lebesuge measurable, where m*(E) denote the Lebesgue Outer Measure of E. ===============
1. 1 answer
2. asked by Ashley
3. 92 views