Let (X, A, µ) and (Y, B, v) be measure spaces. Prove that (a) if E E A x B then y-section of E is measurable. (b) if f : X ×Y→R is a measurable function then y-section of f is measurable.

Q: Let (X, E, µ) be a measure space and let ø, v be nonnegative simple functions. Show that |(6+ v)dµ =…

A:

Q: 2. Let (X,r) and (Y.A) be two topological spaces. Let B be a base for A. Prove that a function f…

A: Given below the detailed solution

Q: Let f [0, 2] → R be a continuous function, with ƒ(0) ≤ f(1) ≤ f(2). Show that there : exists xo [0,…

A:

Q: Let f be a real valued function defined on [a, b] . Let f have a local minimum at a point x ∈ (a, b)…

A:

Q: 3. Let f: R³ R be defined by f(x, y, z) =|| x ||. Find Vf(x, y, z). What is the domain of Vf?

A:

Q: "Prove that the function f : R→ R with ƒ(x) = = is uniformly continuous."

A:

Q: Ja (16) Let f e Lla, b]. Show that if g is a bounded measurable function then fa E Cla bl

A:

Q: Let f(x) be a function continuous on [1, 3] and differentiable on (1, 3), such that f(1) = 1, f(3) =…

A: Given that , f(x) be a function continuous on [1, 3] and differentiable on (1, 3), such that f(1) =…

Q: Let X, Y and Z be sets. A, B are subsets of Y. f:X → Y is a function. Prove the given statement if…

A:

Q: Let f [0, 1] → [0, 1] be continuous. Show that there exists an element x = [0, 1] such that f(x) =…

A:

Q: Let f mapping R into R be a function, and let X be a subset of R2. (a) Define what it means for f…

A: Let f:ℝ→ℝ be a function and let X be a subset of ℝ2 (a) A real-valued function f is said to be…

Q: Let (X, E) be a measurable space and E e E. If E1 e £ is such that E1 C E and ƒ is measurable on E…

A: