Sentence examples for be a measurable function from inspiring English sources

Let ((Omega, Sigma, mu)) be a measure space, (f:Omegarightarrow[0,1]) be a measurable function, and (p:Omegarightarrowmathbb{R}) be a nonnegative integrable function.

Let ((Omega, Sigma, mu)) be a measure space, (f:Omegarightarrow [0,1]) be a measurable function.

Let ((Omega, Sigma, mu)) be a measure space, (f:Omegarightarrow [0,1]) be a measurable function, and C be a copula.

The nonadditive set function μ is a mapping from P X) to [0, ∞) where μ=0. Let f: X→ be a measurable function on the measure space (X, F, μ), whose outputs represent the observed target values.

Let p ∈ L ( [ a, b ] ; R + ), τ : [ a, b ] → [ a, b ] be a measurable function, and let the functional h be defined by formula (4), where λ > 0 and h 0, h 1 ∈ P F a b are such that the inequalities h ( 1 ) > 1, 0 < h 0 ( 1 ) < 1. are fulfilled.

Let g ∈ L ( [ a, b ] ; R + ), μ : [ a, b ] → [ a, b ] be a measurable function, and let the functional h be defined by formula (4), where λ > 0 and h 0, h 1 ∈ P F a b are such that inequalities (11) are fulfilled.

Suppose that f is a measurable function on a measure space.

where is a measurable function.

The obstacle is a measurable function.

If u is a measurable function on ∂ C n satisfying.

for all and, where is a measurable function and is a strictly monotone mapping.