The MIF method exploits the absolute continuity of admissible indemnification functions and formulates optimal reinsurance model into a functional linear programming of determining an optimal measurable function valued over a bounded interval.
The integral average of a measurable function f over Q is written m_{Q}(f)= fint_{Q} f(x),dx= frac{1}{|Q|} int_{Q} f(x),dx.
where is not necessarily continuous, but is such that for every fixed the function is measurable and is of bounded variations over compact interval in and nondecreasing, and is continuous; is a strongly elliptic operator given by (12).
For and a weight, we denote the weighted -norm of a measurable function over by (1.1).
Clinical eligibility criteria were; Histologically confirmed mCRC (adenocarcinomas) refractory to prior chemotherapy, age over 18 years, ECOG performance status ≤ 2, adequate organ function, and measurable disease according to the Response Evaluation Criteria in Solid Tumours (RECIST)[ 18].
with and locally bounded (possibly discontinuous) function and measurable.
Lebesgue measure, measurable functions, integrability, completeness of L-p spaces.
Let J : = [ 0, 1 ] and L 1 ( J, E ) denote the Banach space of real-valued Lebesgue integrable functions on the interval J, L ∞ ( J, E ) denote the Banach space of real-valued essentially bounded and measurable functions defined over J with the norm ∥ ⋅ ∥ L ∞.
Hence, the function (phi( cdot,x)) is ({mathcal{T}}_{mu} -measurable over T (since (mu(Y)=0)).
(a) For all (xin X), the function (f_{n}( cdot,x)) is ({mathcal{T}}_{mu} -measurable over T. To see this, fix (xin X).
Examples of N- measurable functions are Carathéodory functions, Baire measurable functions.
