Question

Problem 1. Let {En}n∞=1 be a sequence of nonempty (Lebesgue) measurable subsets of [0, 1] satisfying...

Problem 1. Let {En}n=1 be a sequence of nonempty (Lebesgue) measurable subsets of [0, 1] satisfying

limn→∞m(En) = 1.

Show that for each ε ∈ [0, 1) there exists a subsequence {Enk }k=1 of {En}n=1 such that m(∩k=1Enk) ≥ ε

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Question 4 Let a sequence {an}∞ n=1 a sequence satisfying the condition ∀c ∈ (0, 1),...
Question 4 Let a sequence {an}∞ n=1 a sequence satisfying the condition ∀c ∈ (0, 1), ∀n ∈ N, | a_(n+2) − a_(n+1) | < c |a_(n+1) − a_n |. 4.1 Show that ∀c ∈ (0, 1), ∀n ∈ N, n ≥ 2, | a_(n+1) − a_n | < c^(n−1) | a_2 − a_1 |. 4.2 Show that {an}∞ n=1 is a Cauchy sequence
Discrete mathematics function relation problem Let P ∗ (N) be the set of all nonempty subsets...
Discrete mathematics function relation problem Let P ∗ (N) be the set of all nonempty subsets of N. Define m : P ∗ (N) → N by m(A) = the smallest member of A. So for example, m {3, 5, 10} = 3 and m {n | n is prime } = 2. (a) Prove that m is not one-to-one. (b) Prove that m is onto.
Let X be a set and let (An)n∈N be a sequence of subsets of X. Show...
Let X be a set and let (An)n∈N be a sequence of subsets of X. Show that: (a) If (An)n∈N is increasing, then liminf An = limsupAn =S∞ n=1 An. (b) If (An)n∈N is decreasing, then liminf An = limsupAn =T∞ n=1 An.
Problem 1 Let {an} be a decreasing and bounded sequence. Prove that limn→∞ an exists and...
Problem 1 Let {an} be a decreasing and bounded sequence. Prove that limn→∞ an exists and equals inf{an}.
Telescoping Series. Let {an} ∞ n=0 be a sequence of real numbers converging to zero, limn→∞...
Telescoping Series. Let {an} ∞ n=0 be a sequence of real numbers converging to zero, limn→∞ an = 0. Let bn = an − an+1. Then the series X∞ n=0 bn converges.
Let (an)∞n=1 be a monotone sequence. Let (ank )∞k=1 be a subsequence of (an). Prove that...
Let (an)∞n=1 be a monotone sequence. Let (ank )∞k=1 be a subsequence of (an). Prove that (an) converges iff (ank) converges. Also, prove that if the two sequences converge, their limits are the same.
Definition: Let p be a prime and 0 < n then the p-exponent of n, denoted...
Definition: Let p be a prime and 0 < n then the p-exponent of n, denoted ε(n, p) is the largest number k such that pk | n. Note: for p does not divide n we have ε(n,p) = 0 Notation: Let n ∈ N+ we denote the set {p : p is prime and p | n} by Pr(n). Observe that Pr(n) ⊆ {2, 3, . . . n} so that Pr(n) is finite. Problem: Let a, b be...
Define a sequence (xn)n≥1 recursively by x1 = 1 and xn = 1 + 1 /(xn−1)...
Define a sequence (xn)n≥1 recursively by x1 = 1 and xn = 1 + 1 /(xn−1) for n > 0. Prove that limn→∞ xn = x exists and find its value.
If (xn) ∞ to n=1 is a convergent sequence with limn→∞ xn = 0 prove that...
If (xn) ∞ to n=1 is a convergent sequence with limn→∞ xn = 0 prove that lim n→∞ (x1 + x2 + · · · + xn)/ n = 0 .
Let A be an n×n matrix. If there exists k > n such that A^k =0,then...
Let A be an n×n matrix. If there exists k > n such that A^k =0,then (a) prove that In − A is nonsingular, where In is the n × n identity matrix; (b) show that there exists r ≤ n such that A^r= 0.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT