Sentence examples for be an absolutely continuous from inspiring English sources

} end{aligned}The main theorem in this setting (originally proven in [3]) relates absolutely continuous curves in (mathbb W_p) with solutions of the continuity equation: Let ((mu _t)_{tin [0,1]}) be an absolutely continuous curve in (mathbb W_p(Omega )) (for (p>1) and (Omega subset mathbb R^d) an open domain).

Let (Phi: I rightarrowmathbb{C}) be an absolutely continuous functions on ([a,b]inmathring{I}), the interior of I.

Lemma 5.1 Let f : [ a, b ] → R be an absolutely continuous mapping for which f ′ ∈ L p [ a, b ], p > 1.

Let (f:[a,b]rightarrow mathbb{R}) be a Lebesgue integrable function and (h:[a,b]rightarrow mathbb{R}) be an absolutely continuous function with ((cdot-a)(b-cdot)[h']^{2} in L[a,b]).

Let (h : [a, b] tomathbb{R}) be a monotonic nondecreasing function and let (g : [a, b] tomathbb{R}) be an absolutely continuous function such that (g^{prime}in L_{infty}[a, b]).

Let (f:[a,b]rightarrowmathbb{R}) be a Lebesgue integrable function and (g:[a,b]rightarrowmathbb{R}) be an absolutely continuous function with ((cdot-a)(b-cdot)[g^{prime }]^{2}in L_{1}[a,b]).

Let f T (t) be the pdf of a continuous random variable T defined on [a, b] and W be a absolutely continuous and monotonically non-decreasing function with W 0) → a and W(1) → b.

Consequently, f is an absolutely continuous CD primitive of the restriction of g to [ a, b ].

Assume that (fin{mathscr{H}}) is a left continuous function and F is an absolutely continuous function satisfying (F'=f).

A pre-Hölder function α : R ¯ + → R ¯ + is an absolutely continuous bijective function satisfying α ( 0 ) = 0.

end{aligned} (4.28)Thus, from Theorem 2.6 we have that (v_E) is an absolutely continuous function in (mathbb {R}).