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Let (X, S, µ) be a measure space and (S, 1·1) a separable Banach space. A function f from X into S will be called simple if it takes only finitely many values, each on a set in S. Let g be any measurable function from X into S such that ( 1g1 dµ<>∞. Show that there exist simple functions fn with ( 1 fn - g1 dµ → 0 as n → ∞. If f is simple with f (x ) = ),1≤i ≤ n 1A(i )(x )si for si ∈ S and A(i ) ∈ S, let ( f dµ = ),1 ≤ i ≤ n µ( A(i ))si ∈ S. Show that ( f dµ is well-defined and if ( 1 fn - g1 dµ → 0, then ( fn dµ converge to an element of S depending only on g, which will be called ( g dµ (Bochner integral).
This study investigates whether there are differences in the outcomes of three different treatments for anxiety
Solve the initial value problem y' = 2y + 3, y(0) = 2. The population p(t) of the South American Agouti satisfied the population law dp/dt = 0.05p - 450, where the factor 0.05 reflects the birth rate and the -450 is a constant harvest rate due to ..
Construct a 95% confidence interval estimate for the mean yield of five-year certificates of deposit.
sixty percent of all vehicles examined at a certain emissions inspection station pass the inspection. assuming that
The mean and standard deviation of these scores are 23.0 and 5.0 respectively. The test was administered to 100 students. What is the T-score equivalent to the raw-score 13?
What is the p-value and compute a 95% CI for the difference in means between the two groups?
Solve the following questions involving fundamental operations on polynomials. Solve the following problems involving applications of polynomials.
What are accruals? Provide examples of accruals. Why do accruals require adjusting entries? What types of accounts are debited and credited in an unearned revenue adjusting entry?
a clothing store chain is having a sale based on the use of a coupon. the company is interested in knowing whether the
the average tenure of technicians at abc company is 10 years with a standard deviation of 5 years. calculate the
Past studies have revealed that only 88% of booked passengers actually arrive for flight.) Determine probability that if airline books 17 persons, not adequate seats will be available.
A firm plans to hire 100 employees during the year. It expects that 25 of these employees will obtain graduate degrees within the next 5 years of being hired.
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