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...

(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...

Lebesgue-measurable functions does not have to be Lebesgue-measurable as well. Nevertheless, a composition of a measurable function with a continuous function...

measurable selection theorem is a result from measure theory that gives a sufficient condition for a set-valued function to have a measurable selection...

≤ 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)...

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...

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

logicians, give precise definitions for these weakly specified functions. These generalized functions may be critical in the development of a formalization...

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

is similar but is applied to a non-negative measurable function rather than to an integrable function over its domain. The Fubini and Tonelli theorems...

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

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...

a stationary set of measurable cardinals, and thus it is a Mahlo cardinal. However, the first Woodin cardinal is not even weakly compact. The hierarchy...

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

{\displaystyle \circ } takes two functions, f {\displaystyle f} and g {\displaystyle g} , and returns a new function h ( x ) := ( g ∘ f ) ( x ) = g (...

continuous at each θ ∈ Θ for almost all xs, and measurable function of x at each θ. there exists a dominating function d(x) such that E[d(X)] < ∞, and ‖ f ( x...

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...

been viewed as a discrete analogue of Lyapunov's theorem. Bochner measurable function Bochner integral – Concept in mathematics Bochner space – Type of...

that says that for sequences of non-negative pointwise-increasing measurable functions 0 ≤ f 1 ( x ) ≤ f 2 ( x ) ≤ ⋯ {\displaystyle 0\leq f_{1}(x)\leq f_{2}(x)\leq...

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...

(f(x)\in F(x))\,.} The existence of more regular choice functions, namely continuous or measurable selections is important in the theory of differential...

theorem relates the weak convergence of cumulative distribution functions to the convergence of expectations of certain measurable functions. It is named after...

}}_{\geq 0}})} -measurable non-negative functions f n : X → [ 0 , + ∞ ] {\displaystyle f_{n}:X\to [0,+\infty ]} . Define the function f : X → [ 0 , +...

subsets of the Cantor space are measurable and have the property of Baire and thus that no infinite parity function exists; this holds in the Solovay...

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

mixing implies weak mixing. Furthermore, weak mixing (and thus also strong mixing) implies ergodicity: that is, every system that is weakly mixing is also...

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