measurable function

Related BrainMass Solutions

• Prove Functions and Sets

  1b. prove directly that f and f are non-negative measurable function on E with f(x) = f (x) - f (x). 2b. prove that = and that is measurable. 3b. if f is areal- valued function on [a, b] such that is measurable on [a, b] is f measurable

• Measurable function

  Proof First, if , that is, is the point-wise limit of simple functions, then check that , then is measurable. Now let be a measurable function. We fix and define , These sets are measurable. Now let .

• Real Analysis : Lebesgue Measure

  Hence h is a simple function. Similarly, the product function defined by is also measurable as f,g are measurable. And the range of k is atmost the cardinality of f(A)Xg(B). Hence k is also a simple function.

• Real Analysis : Measurable Sets and Functions

  If E is measurable set in X and if X_E ( x) = { 1 if x is in E, 0 if x is not in E} then X_E is a measurable function.

• Borel-measurable function

  50105 Borel-measurable function Prove that the following function is Borel-measurable function.

• Measurable Spaces and Properties of Integrals of Simple Functions

  54240 Measurable Spaces and Properties of Integrals of Simple Functions 1).If A is a subset of B, A,B in m ( measurable sets) then show that integral (region A) s dM =< integral ( region B) s dM Where s here is a simple non-negative measurable function

• Real analysis proofs

  Since all are measurable, then are measurable sets. Hence is measurable. Therefore, is a measurable function. There are two real analysis proofs here, one regarding unions and supremum and one regarding measurable functions.

• Measurable functions

  46689 Problems with measurable functions 1) a. If g is measurable on [a, b] with g(x) 0 for all x [a, b], prove that 1/g is measurable on [a, b]. b. prove that every continuous real- valued function f on [a, b] is measurable.

• Counting measure

  function defined over an abstract (measurable) set A.