Weakly measurable function information

analysis—a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function...

and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure...

Bochner-measurable function taking values in a Banach space is a function that equals almost everywhere the limit of a sequence of measurable countably-valued...

called weakly measurable if for all φ ∈ V ′ , {\displaystyle \varphi \in V',} the scalar-valued map φ ∘ f {\displaystyle \varphi \circ f} is a measurable map...

complex onePages displaying short descriptions of redirect targets Weakly measurable function Evans, Lawrence C. (1998). Partial differential equations. Providence...

space – Type of topological space Bochner measurable function Pettis integral Vector measure Weakly measurable function Diestel, Joseph; Uhl, Jr., John Jerry...

every n > N and for every measurable set A. As before, this implies convergence of integrals against bounded measurable functions, but this time convergence...

(they are in fact weakly Mahlo). All measurable cardinals are real-valued measurable, and a real-valued measurable cardinal κ is measurable if and only if...

been viewed as a discrete analogue of Lyapunov's theorem. Bochner measurable function Bochner integral Bochner space – Type of topological space Complex...

Continuity: for every profile v, the set of profiles weakly better than v and the set of profiles weakly worse than v are closed sets.[jargon] 4. Independence...

lifting to a ‘weakly’ measurable function with values in a weakly compact set of a Banach space, one obtains a strongly measurable function; this gives...

In mathematics, function composition is an operation  ∘  that takes two functions f and g, and produces a function h = g  ∘  f such that h(x) = g(f(x))...

≤ p ≤ ∞ {\displaystyle 1\leq p\leq \infty } , is the Lp space of measurable functions whose p-norm ‖ f ‖ p = ( ∫ R | f | p ) 1 / p {\textstyle \|f\|_{p}=\left(\int...

{\displaystyle \{s\in S:f(s)\neq g(s)\}} is measurable and has measure zero. Similarly, a measurable function f {\displaystyle f} (and its absolute value)...

: 314, 319  Martingales are weakly dependent [citation needed], so many results about martingales also hold true for weakly dependent sequences. An example...

non-measurable sets, which states that there exists a subset of the real numbers that is not Lebesgue measurable. There exist Lebesgue-measurable subsets...

} This condition is only slightly weaker than convexity. For example, a real-valued Lebesgue measurable function that is midpoint-convex is convex: this...

with weaker notions of locally compact. Every closed set in a weakly locally compact space (= condition (1) in the definitions above) is weakly locally...

Ramseyness and measurability is existence of a κ-complete normal non-principal ideal I on κ such that for every A ∉ I and for every function f: [κ]<ω → {0...

In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all...

any orthonormal sequence {fn} converges weakly to 0, as a consequence of Bessel's inequality. Every weakly convergent sequence {xn} is bounded, by the...

the collector) then a measurable electric current will be observed. Thermionic emission can be used to measure the work function of both the hot emitter...