Question

Let f be a function with measurable domain D. Then f is measurable if and only...

Let f be a function with measurable domain D. Then f is measurable if and only if the function g(x)={f(x) if x\in D ,0 if x \notin D } is measurable.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

HHere is the solution

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A function f is said to be Borel measurable provided its domain E is a Borel...
A function f is said to be Borel measurable provided its domain E is a Borel set and for each c, the set {x in E l f(x) > c} is a Borel set. Prove that if f and g are Borel measurable functions that are defined on E and are finite almost everywhere on E, then for any real numbers a and b, af+bg is measurable on E and fg is measurable on E.
Let (X, A) be a measurable space and f : X → R a function. (a)...
Let (X, A) be a measurable space and f : X → R a function. (a) Show that the functions f 2 and |f| are measurable whenever f is measurable. (b) Prove or give a counterexample to the converse statement in each case.
Let f and g be measurable unsigned functions on R^d . Assume f(x) ≤ g(x) for...
Let f and g be measurable unsigned functions on R^d . Assume f(x) ≤ g(x) for almost every x. Prove that the integral of f dx ≤ Integral of g dx.
A function f on a measurable subset E of Rd is measurable if for all a...
A function f on a measurable subset E of Rd is measurable if for all a in R, the set f-1([-∞,a)) = {x in E: f(x) < a} is measurable Prove or disprove the following functions are measurable: (a) f(x) = 8 (b) f(x) = x + 2 (c) f(x) = 3x (d) f(x) = x2
Let (X , X) be a measurable space. Show that f : X → R is...
Let (X , X) be a measurable space. Show that f : X → R is measurable if and only if {x ∈ X : f(x) > r} is measurable for every r ∈ Q.
A function f on a measurable subset E of Rd is measurable if for all a...
A function f on a measurable subset E of Rd is measurable if for all a in R, the set f-1([-∞,a)) = {x in E: f(x) < a} is measurable Prove that if f is continuous on Rd then f is measurable
Problem 2. Let F : R → R be any function (not necessarily measurable!). Prove that...
Problem 2. Let F : R → R be any function (not necessarily measurable!). Prove that the set of points x ∈ R such that F(y) ≤ F(x) ≤ F(z) for all y ≤ x and z ≥ x is Borel set.
Let the function f and g be defined as f(x) = x/ x − 1 and...
Let the function f and g be defined as f(x) = x/ x − 1 and g(x) = 2 /x +1 . Compute the sum (f + g)(x) and the quotient (f/g)(x) in simplest form and describe their domains. (f + g )(x) = Domain of (f+g)(x): (f/g)(x) = Domain of (f/g)(x):
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let...
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let f : A → B and g : B → A be defined as follows: f = {(a, c), (e, e), (g, d)} g = {(c, a), (d, e), (e, e), (f, a), (g, g)} (a) Consider the composed function g ◦ f. (i) What is the domain of g ◦ f? What is its codomain? (ii) Find the function g ◦ f. (Find...
4. Let f be a function with domain R. Is each of the following claims true...
4. Let f be a function with domain R. Is each of the following claims true or false? If it is false, show it with a counterexample. If it is true, prove it directly from the FORMAL DEFINITION of a limit. (a) IF limx→∞ f(x) = ∞ THEN limx→∞ sin (f(x))  does not exist. (b) IF f(−1) = 0 and f(1) = 2 THEN limx→∞ f(sin(x)) does not exist.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT