"I believe this is an important milestone in the field of mRNA therapeutics as it starts to address many questions regarding the safety and delivery of mRNA to human tissues, the duration and level of the protein that can be expressed and the ability of the technology to have a physiologic,

measurable function over a prolonged period of time," said Kenneth Chien, M.D., Ph.D., a professor in the Department of Cell and Molecular Biology and the Integrated Cardio Metabolic Center at the Karolinska Institute in Stockholm, a Moderna scientific co-founder and co-author on the paper.

The exponent p(x) is a given

measurable function on [bar.[OMEGA]] such that

Variable Lebesgue spaces are a generalization of the Lebesgue spaces that allow the exponents to be a

measurable function and thus the exponent may vary.

A

measurable function f : [OMEGA] [right arrow C is called a random fixed point for the operator T : [OMEGA] x C [right arrow] C if T([omega], f([omega])) = f([omega]).

(i) For any nonnegative

measurable function f(x) in R, we have the following inequality:

For a finite valued function u [member of] [L.sup.0] ([SIGMA]), the weighted composition operator W on [L.sup.p] ([SIGMA]) with 1 [less than or equal to] p [less than or equal to] [infinity], induced by u and the non-singular

measurable function [phi] is given by W = [M.sub.u] [??] [C.sub.[phi]] where [M.sub.u] is a multiplication operator and [C.sub.[phi]] is a composition operator on [L.sup.p] ([SIGMA]) defined by [M.sub.u]f = uf and [C.sub.[phi]]f = f [??] [phi], respectively.

where a and b are Lebesgue measurable essentially bounded on [0, [infinity]) functions, and there exists [tau] > 0 such that the

measurable function h satisfies 0 [less than or equal to] t - h(t) [less than or equal to] [tau].

If [[iota].sup.2] is

measurable function, then A = [([[iota].sup.2]).sup.-1] ([N.sub.e]) is a measurable set, where [N.sub.e] = {x [member of] B(H) : [absolute value of (<xe, e>)] < 1}.

Where [mathematical expression not reproducible] and f : J x E x E x [OMEGA] [right arrow] E are given continuous functions, ([OMEGA], A, v) is a measurable space, and E is a real (or complex) Banach space with norm [[parallel] * [parallel].sub.e] and dual [E.sup.*], such that E is the dual of a weakly compactly generated Banach space [mathematical expression not reproducible], is the left-sided mixed Hadamard integral of order r, and [mathematical expression not reproducible] is a given continuous and

measurable function such that

(2) For any bounded, Borel

measurable function g(x),

Let f : X [right arrow] [0, [infinity]) be a

measurable function (i.e., {f [greater than or equal to] [alpha]} [member of] A for any [alpha] [greater than or equal to] 0).

Let {P(x,y,A) : x, y [member of] X, A [member of] F} be a family of functions on X x X x F such that, for any fixed x,y [member of] X P(x, y,*) [member of] S(X, F), P(x, y, A) regarded as a function of two variables x and y with fixed A [member of] F is a

measurable function on (X x X, F [cross product] F) and P(x, y, A) = P(y, x, A) for any x, y [member of] X and A [member of] F.