1 дек. 2022 г. · Measurability of a Bochner measurable Lp-valued function is measurable. we have that fn(t)→w(t) in Lp(Rn) for every t>0.

15 янв. 2014 г. · I believe that the composition t↦f(t,g(t)) is measurable only if f is Borel measurable and g is Lebesgue or Borel measurable.

3 мар. 2014 г. · I have the following problem. Let (Σ,Ω,μ) be a measure space and let X be a Banach space. Take a function f:Ω→B(X), which takes values in ...

21 окт. 2013 г. · The strongly measurable functions are the ones which can be pointwise approximated everywhere by simple functions "nicely" (f=limfn and |fn|≤|f|) ...

7 сент. 2013 г. · A function f:Ω→X is μ-measurable if it is the limit of a sequence of μ-measurable simple functions (almost everywhere).

1 дек. 2021 г. · Let f:Ω→B be Bochner-measurable, i.e. the point-wise limit of a sequence of simple (i.e. countably-valued measurable) functions (sn). I ...

7 дек. 2017 г. · The function R first needs to be strongly μ-measurable in the sense of Bochner integrals. By Pettis' Theorem, this means R(x) needs to be μ-almost-everywhere ...

3 июн. 2023 г. · Yes, you can develop a lot of the basic/standard theory without completeness of the measure, and indeed not having to complete measures is nice.

20 мая 2013 г. · As long as R(t) is otherwise arbitrary, the answer is no. Take a non-measurable set E and put R(t)={Rt∈E−Rt∉E.

5 окт. 2018 г. · Theorem. If μ is σ-finite, f is Bochner measurable if and only if f is limit μ-almost everywhere of a sequence of integrable simple functions.