Please show the steps thoroughly, thank you so much!
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Please show the steps thoroughly, thank you so much! Let X be a compact Hausdorff space...
Use Alaoglu's theorem to show that if X is a Banach space, there is some compact...
Use Alaoglu's theorem to show that if X is a Banach space, there is some compact space Y such that X is isometrically isomorphic to a closed subspace of C(Y). HINT: What set is compact in Alaoglu's theorem?
Use Alaoglu's theorem to show that if X is a Banach space, there is some compact space Y such that X is isometrically isomorphic to a closed subspace of C(Y). HINT: What set is compact in Alaoglu's theorem?
(3) Let X be a locally compact Hausdorff space, let A be a ơ-algebra on X that includes B(X) and let μ be a regular measure on (Χ.Α). Show that the completion of μ is regular. (3) Let X be a loc...
(3) Let X be a locally compact Hausdorff space, let A be a ơ-algebra on X that includes B(X) and let μ be a regular measure on (Χ.Α). Show that the completion of μ is regular.
(3) Let X be a locally compact Hausdorff space, let A be a ơ-algebra on X that includes B(X) and let μ be a regular measure on (Χ.Α). Show that the completion of μ is regular.
(2) Let X be a locally compact Hausdorff space, and let μ be a regular Borel measure on X such that μ(X) = +oo. Show that there is a non-negative function f CO(X) such that Jfdlı-+oo. Idea. Construct...
(2) Let X be a locally compact Hausdorff space, and let μ be a regular Borel measure on X such that μ(X) = +oo. Show that there is a non-negative function f CO(X) such that Jfdlı-+oo. Idea. Construct a sequence {K f-Σ001 nzfn, n} of disjoint compact sets K n with μ(An) > n and set where fn E Co(X) with XKn S f 31 く!
(2) Let X be a locally compact Hausdorff space, and let μ be a...
1.5.7 Prove the following separately Theorem 1.5.10. Let (X,d) be a metric space. (a) IfY is...
1.5.7 Prove the following separately Theorem 1.5.10. Let (X,d) be a metric space. (a) IfY is a compact subset of X, and Z C Y, then Z is compact if and only if Z is closed (b) IfY. Y are a finite collection of compact subsets of X, then their union Y1 U...UYn is also compact. (c) Every finite subset of X (including the empty set) is compact.
(a) Suppose K is a compact subset of a metric space (X, d) and x є X but x K Show that there exist disjoint, open subsets of Gi and G2 of (X, d) such that r E Gi and KG2. (Hint: Use the version of co...
(a) Suppose K is a compact subset of a metric space (X, d) and x є X but x K Show that there exist disjoint, open subsets of Gi and G2 of (X, d) such that r E Gi and KG2. (Hint: Use the version of compactness we called "having a compact topology." You will also need the Hausdorff property.) b) Now suppose that Ki and K2 are two compact, disjoint subsets of a metric space (X, d). Use (a)...
A. Let (X, d) be a metric space so that for every E X and every...
A. Let (X, d) be a metric space so that for every E X and every r>0 the closed ball N,(z) = {ye X : d(y, z) < r} is com pact. Let be a homeomorphism. (1) Prove that f"-+m-fn。fm for all n, m E Z. (2) Let z E X and suppose that F, {fn (z) : n E 2) is a closed subset of X Prove that F is a discrete subset of X (A subset Y C...
Please answer in the style of a formal proof and thoroughly reference any theorems, lemmas or...
Please answer in the style of a formal proof and thoroughly
reference any theorems, lemmas or corollaries utilized.
BUC
stands for bounded uniformly continuous
Let (X, d) be a metric space. Show that the set V of Lipschitz continu- ous bounded functions from X to R is a dense linear subspace of BUC(X, R). Since, in general, V #BUC(X, R), V is not a closed subset of BUC(X, R). Hint: For f EBUC(X, R) define the sequence (fr) by fn(x)...
QUESTION 26 AND 31 PLEASE SHOW STEPS THANK YOU SO MUCH J-2 J-V4-z² Ji 26. Let...
QUESTION 26 AND 31 PLEASE SHOW STEPS THANK
YOU SO MUCH
J-2 J-V4-z² Ji 26. Let be the region below the paraboloid x2 + y? = z – 2 %3D that lies above the part of the plane * + Y + z = I in the first octant. Express f (x, y, z) dV as an iterated integral (for an arbitrary function J). 27. Assume J (ª, Y, 2) can be expressed as a product, f (x, y, z)...
Please use Precaulc to solve and show steps. Thank you 1. Let f(x) = *** a)...
Please use Precaulc to solve and show steps. Thank you
1. Let f(x) = *** a) Find f-'(x), if it exits b) show that f(--(x)) = x c) Sketch NEAT graphs of both functions below, labeling their intercepts, asymptotes etc. y = f(x) y = f'(x) d) Write the intervals of the functions below Domain of f(x) Domain off-(x) Range of f(x) Range of f-'(x)
Please answer the following statistics problem and show all your steps thoroughly! Thank you! Question...
Please answer the following statistics problem and show
all your steps thoroughly! Thank you!
Question 5 (10 marks) Suppose that (X, Y) have joint probability function f(x,y) specified by the following table: f(x,y) 0 0.2 0.15 1 Х 2 0.3 0 1 0.1 0.1 3 0.05 0.1 у 2 a) (2 marks) Find the marginal distribution of X and Y (display in a table) b) (2 marks) Find the conditional distribution of Y given X=3. (display in a table)...
Use Alaoglu's theorem to show that if X is a Banach space, there is some compact space Y such that X is isometrically isomorphic to a closed subspace of C(Y). HINT: What set is compact in Alaoglu's theorem?
Use Alaoglu's theorem to show that if X is a Banach space, there is some compact space Y such that X is isometrically isomorphic to a closed subspace of C(Y). HINT: What set is compact in Alaoglu's theorem?
(3) Let X be a locally compact Hausdorff space, let A be a ơ-algebra on X that includes B(X) and let μ be a regular measure on (Χ.Α). Show that the completion of μ is regular.
(3) Let X be a locally compact Hausdorff space, let A be a ơ-algebra on X that includes B(X) and let μ be a regular measure on (Χ.Α). Show that the completion of μ is regular.
(2) Let X be a locally compact Hausdorff space, and let μ be a regular Borel measure on X such that μ(X) = +oo. Show that there is a non-negative function f CO(X) such that Jfdlı-+oo. Idea. Construct a sequence {K f-Σ001 nzfn, n} of disjoint compact sets K n with μ(An) > n and set where fn E Co(X) with XKn S f 31 く!
(2) Let X be a locally compact Hausdorff space, and let μ be a...
1.5.7 Prove the following separately Theorem 1.5.10. Let (X,d) be a metric space. (a) IfY is a compact subset of X, and Z C Y, then Z is compact if and only if Z is closed (b) IfY. Y are a finite collection of compact subsets of X, then their union Y1 U...UYn is also compact. (c) Every finite subset of X (including the empty set) is compact.
(a) Suppose K is a compact subset of a metric space (X, d) and x є X but x K Show that there exist disjoint, open subsets of Gi and G2 of (X, d) such that r E Gi and KG2. (Hint: Use the version of compactness we called "having a compact topology." You will also need the Hausdorff property.) b) Now suppose that Ki and K2 are two compact, disjoint subsets of a metric space (X, d). Use (a)...
A. Let (X, d) be a metric space so that for every E X and every r>0 the closed ball N,(z) = {ye X : d(y, z) < r} is com pact. Let be a homeomorphism. (1) Prove that f"-+m-fn。fm for all n, m E Z. (2) Let z E X and suppose that F, {fn (z) : n E 2) is a closed subset of X Prove that F is a discrete subset of X (A subset Y C...
Please answer in the style of a formal proof and thoroughly
reference any theorems, lemmas or corollaries utilized.
BUC
stands for bounded uniformly continuous
Let (X, d) be a metric space. Show that the set V of Lipschitz continu- ous bounded functions from X to R is a dense linear subspace of BUC(X, R). Since, in general, V #BUC(X, R), V is not a closed subset of BUC(X, R). Hint: For f EBUC(X, R) define the sequence (fr) by fn(x)...
QUESTION 26 AND 31 PLEASE SHOW STEPS THANK
YOU SO MUCH
J-2 J-V4-z² Ji 26. Let be the region below the paraboloid x2 + y? = z – 2 %3D that lies above the part of the plane * + Y + z = I in the first octant. Express f (x, y, z) dV as an iterated integral (for an arbitrary function J). 27. Assume J (ª, Y, 2) can be expressed as a product, f (x, y, z)...
Please use Precaulc to solve and show steps. Thank you
1. Let f(x) = *** a) Find f-'(x), if it exits b) show that f(--(x)) = x c) Sketch NEAT graphs of both functions below, labeling their intercepts, asymptotes etc. y = f(x) y = f'(x) d) Write the intervals of the functions below Domain of f(x) Domain off-(x) Range of f(x) Range of f-'(x)
Please answer the following statistics problem and show
all your steps thoroughly! Thank you!
Question 5 (10 marks) Suppose that (X, Y) have joint probability function f(x,y) specified by the following table: f(x,y) 0 0.2 0.15 1 Х 2 0.3 0 1 0.1 0.1 3 0.05 0.1 у 2 a) (2 marks) Find the marginal distribution of X and Y (display in a table) b) (2 marks) Find the conditional distribution of Y given X=3. (display in a table)...
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