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This is proven in Rademacher and Toeplitz (1957).

A Liouville Space, also known as line space or "extended" Hilbert space, it is the Cartesian product of two Hilbert spaces.

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.

A function f such that |f(x)-f(y)|<=C|x-y| for all x and y, where C is a constant independent of x and y, is called a Lipschitz function. For example, any function with a ...

int_0^inftye^(-ax)J_0(bx)dx=1/(sqrt(a^2+b^2)), where J_0(z) is the zeroth order Bessel function of the first kind.

A list is a data structure consisting of an ordered set of elements, each of which may be a number, another list, etc. A list is usually denoted (a_1, a_2, ..., a_n) or ...

A statement letter or a negation of a statement letter (Mendelson 1997, p. 30).

Little-omega notation is the inverse of the Landau symbol o, i.e., f(n) in o(phi(n)) <==> phi(n) in omega(f(n)).

A roll of 4 on a pair of six-sided dice in the game of craps (Gardner 1978, p. 256). The probability of rolling "a little Joe" is 1/12, or 8.333...%. A roll of "4 the hard ...