Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [2n-1 3n+1]}, be a family of elements of B(R). Then µ(U +, an-1]) equals Šn=1 [n+ n=11 a.0 b.1 c.3 d.4 a O b O d

Q: 0 if x = y o(x, y) 1 if x #y x, y ER". The open ball in the discrete metric space R", o> is the…

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Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A,n = [7n-1, 12n+1]} be a family of…

A: Given: (X,B(R),μ) is a Borel measure space.An=7n-1n,12n+1nn=1∞ is a family of elements of B(R).

Q: 4 1 Jl pdf. Let AcR be bounded and set - A=(-a:a E A). Which step of the proof of sup(-A) = - inf(A)…

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Q: 3. Let SP(la, b, c,d.e) and define W:SXSS as the union function: (A, B)AUB. for ill (A. B) ESXS. (a)…

A: Given: S=P({a, b, c, d, e})Define A:S×S→Ssuch thatA(A, B)=A∪Bfor all (A, B)∈S×S We see that S is a…

Q: Exercise 4.2 Let m be Lebesgue measure and A a Lebesgue mea- surable subset of R with m(A) 0. Show…

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Q: 1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and…

A: a) The given set is,S=n-1n:n∈ℕ

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [ Then u(Un+l in 1) equals a.1 7n-1…

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Q: (H.W) let X=Rbe amatric space show that the folloowing subset of Rare сотраct or not 1 1 1- E,=|1 -…

A: We have to find the subset is compact or not

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [2n-1, 3n+1]} be a family of…

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Q: 1- iz If z = x +i y and w = z-i show that |w| = 1-z is purely real

A: i2 = -1

Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A n (A)° = Ā – int A…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: For which of the following space the unit ball is weakly compact a) ℓ2; b) ℓ1; c) C[0, 1]; d) ℓ∞; e)…

A: We are given four spaces. We asked to check in which space a unit ball is weekly compact.Weekly…

Q: 5. Let (X, B(R), µ) be a Borel measure space. Suppose that {An = ["+1, 4n-1]}, be a family of…

A: Let (X, B(R), µ) be a Borel measure space

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that{An = [2n-1 3n+1]]∞ Then µ(U("1, 4n-1])…

A: Borel set means union of sets also an element of that set is also an element of that set, From that…

Q: If Z; is i.i.d N(0,y²) and X1~ N(0,o²) be independent of all Z's. Let Xi+1 = pX;+Z; for all i = 1,2,…

A: From the given information, The provided information are as follows: Zi~i.i.dN0,γ2X1~N0,σ2Zi and X1…

Q: (a) Let E = {q E Q : /2 <q< 4}. Find sup E, inf E, max E, and min E if they exist. (b) Let E =…

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Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A n (A)° = A – int A…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [2n-1 3n+l]}, be a family of…

A: Borel set means we know that those sets satisfying measure conditions. But we don't know about other…

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [Tn-1 12n+1]}, be a family of…

A: Please Check the answer in next step.

Q: Y1 Y2 ER3 [Y3. (x, y) : 2x1Y1 + x2Y2 + 5x3Y3, for x = X2 ,y = X3 (a) Show that S = is an orthogonal…

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Q: 3.20 Composition with an affine function. Show that the following functions f: R" -→R are convex.…

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Q: a) Give a condition on two variables X and Y such that E[XY] = E[X]E[Y]. %3D Suppose that X…

A: Given,a) Let, M be random variable which is independent   of X and Y such that , E(M) = 0    Now,…

Q: A S O Consi der Hhe folhning {(01), (-1,)}, B = [x]e - [;] %3D O find the fransi tion matria from B…

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Q: metoix space and d[211?(₂) for all ₁2 ER 2,12₂ 17. (*/ 1²(₂) d is matrie X. let (Xid) be d' XXR…

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Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A O (A)° = A – int A…

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Q: c) Let R2 have the weighted Euclidean inner product, = 2uV1 + 3u2v2, and let u = (1,1), v = (3,2),…

A: We have been given the inner product as  &lt;u, v&gt; = 2u1v1 + 3u2v2 And u = (1, 1), v = (3, 2), w…

Q: (e) A = (-1,1)U{2} in the standard topology on R %3D (f) A = (-1,1) U {2} in the lower limit…

A: Definition:(1) Limit points: Let (X, τ) be a topological space, a∈X is the limit pointof the set…

Q: - Let X, Y be Banach spaces. We call an operator TE B(X,Y) invertible if there exists an operator…

A: Consider the provided question,Let X,Y be Banach spaces.We call an operator T∈BX,Y invertible,If…

Q: Jina does a weekly exercise program consisting of cardiovascular work and weight training. Each…

A: topic - inequality The given data are: Let x denotes the time (in hours) that Jina spending doing…

Q: 8. Let S= I+T*T: H- H, where T is linear and bounded. Show that s1: S(H)– → H exists.

A: Let S=I+T*T : H→H where T is linear and bounded. Since T is a bounded linear operator and…

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [7n=1 12n+1|0 Then µ(U"1 in-1])…

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Q: Q) let P aprobabiity funckion on S: La,a,a) Find plai) If:- i) pcaz) = and plas) = ii) pc{ãa, az} ,…

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Q: 8. (a) Suppose f : [a, b] → R is integrable and L(ƒ, P) = U(ƒ, P) for some partition P of [a, b].…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Let {X,}neN be a symmetric random walk (X„ = ±1 w.p. 1/2) on (-0o, 1]nZ. Set S, = E X- a) Show that…

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Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, [n-1, 12n+1]}, be a family of elements…

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Q: 2. Let U = {a + bx + cx2 + d³ e P3 (R) | a- 6+d3D0}, and let W = {a + bx + ca? + dx³ e P3(R)| a + 2c…

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Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [7n-1, 12n+1]}, be a family of…

A:

Q: 5. Let (X, B(R), µ) be a Borel measure space. Suppose that {A,, = ["+1, 4n-1]}" be a family of…

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Q: Let (X, B(R), µ) be a Borel measure space. Suppose that {An = [In-1 12n+1]}, be a family of elements…

A: Given, An=7n-n,12n+1nn=1∞ We need to find the value of μ=Un=1∞n+1n,4n-1nn=1∞

Q: Q5. Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = ["+1_ 4n-1 Show that A1 C A2 C…

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Q: (b) Show that Ran(T) is not closed in (. Hint. First show MC Ran(T) Ç co for M := {(y1, , Yn,0,0,…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Q5. Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = ["+1, 4n-1]}" be a family of…

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Q: Exercise 4.2 Let m be Lebesgue measure and A a Lebesgue mea- surable subset of R with m(A) 0. Show…

A: Given that m is a Lebesgue measure and A be a measurable set with m(A) &lt; ∞.

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {An = [2n-1, 3n+1]} be a family of…

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Q: Determine the largest subset S of C where the function ƒ(z)=3x² + 2x−3y² −1+i(6xy+2y) is analytic;…

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Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [2n-1, 3n+1]} be a family of…

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Q: 2. (U) The set A is not compact in the space X. Show explicitly that A has neither the Heine-Borel,…

A: Let S be any subset of ℝn. S satisfies the Heine-Borel property if every open cover of S can be…

Q: Let R:= [0, 1] × [0,1] and let E:= {(x, y) E R|0<ys z} and observe that EC R. a. Find a sequence of…

A: Part(a): Given, R:=0,1×0,1 and the set E:=x,y∈R|0≤y≤x Part(a): R=0,1×0,1 Now,…

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [7n-1, Then u(U l in-1) equals…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.