Question

Show that if µ is countably additive non negative set function on a ring S(X) of...

Show that if µ is countably additive non negative set function on a ring S(X) of subsets of the set X, and finite on some set, then µ is a measure

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
Prove that a disjoint union of any finite set and any countably infinite set is countably...
Prove that a disjoint union of any finite set and any countably infinite set is countably infinite. Proof: Suppose A is any finite set, B is any countably infinite set, and A and B are disjoint. By definition of disjoint, A ∩ B = ∅ Then h is one-to-one because f and g are one-to one and A ∩ B = 0. Further, h is onto because f and g are onto and given any element x in A ∪...
Suppose the sum of some set X of 5 non-negative integers is 51. Show that there...
Suppose the sum of some set X of 5 non-negative integers is 51. Show that there must be a subset of four of them with sum at least 41.
Suppose S is a ring with p elements, where p is prime. a)Show that as an...
Suppose S is a ring with p elements, where p is prime. a)Show that as an additive group (ignoring multiplication), S is cyclic. b)Show that S is a commutative group.
A function f : R → R is called additive if f(x + y) = f(x)...
A function f : R → R is called additive if f(x + y) = f(x) + f(y) for all x, y ∈ R. Is the set of all additive functions a subspace of F(R, R)? Give a proof of counter example.
Let X be a set and A a σ-algebra of subsets of X. (a) A function...
Let X be a set and A a σ-algebra of subsets of X. (a) A function f : X → R is measurable if the set {x ∈ X : f(x) > λ} belongs to A for every real number λ. Show that this holds if and only if the set {x ∈ X : f(x) ≥ λ} belongs to A for every λ ∈ R. (b) Let f : X → R be a function. (i) Show that if...
Define:   x0  = [  r/ (r+2)]  x+r .  Show that  x0   is biased for   µ  in finite            &
Define:   x0  = [  r/ (r+2)]  x+r .  Show that  x0   is biased for   µ  in finite                            samples,  but that it is unbiased for  µ  asymptotically ( as  r  tends to  infinity.).
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.
Part II True or false: a. A surjective function defined in a finite set X over...
Part II True or false: a. A surjective function defined in a finite set X over the same set X is also BIJECTIVE. b. All surjective functions are also injective functions c. The relation R = {(a, a), (e, e), (i, i), (o, o), (u, u)} is a function of V in V if V = {a, e, i, o, u}. d. The relation in which each student is assigned their age is a function. e. A bijective function defined...
Show that if X is an infinite set, then it is connected in the finite complement...
Show that if X is an infinite set, then it is connected in the finite complement topology. Show that in the finite complement on R every subspace is compact.
Let X be a non-empty finite set with |X| = n. Prove that the number of...
Let X be a non-empty finite set with |X| = n. Prove that the number of surjections from X to Y = {1, 2} is (2)^n− 2.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT