Sentence examples for set of real functions from inspiring English sources

C ( M ) is the set of real functions continuous on M. AC ( M ) is the set of real functions absolutely continuous on M. L 1 [ a, b ] is the set of real functions Lebesgue integrable on [ a, b ].

L ∞ [ a, b ] is the set of real functions essentially bounded on [ a, b ].

BV [ a, b ] is the set of real functions with bounded variation on [ a, b ].

Here C ( J ) denotes the set of real functions which are continuous on the interval J.

Let M ⊂ R n, n ∈ N, [ a, b ] ⊂ R. C ( M ) is the set of real functions continuous on M. AC ( M ) is the set of real functions absolutely continuous on M. L 1 [ a, b ] is the set of real functions Lebesgue integrable on [ a, b ].

Now, we consider a new set of real functions, say Θ. Precisely, we modify the set Ψ by substituting the condition (psi_{3}) by another condition.

For example, in 1883, Cantor had assumed (without remark) that the set of all real functions has the size of the third number-class.

Let (X=C[0,T]) be the set of continuous real functions defined on ([0,T]).

B(S) is the set of bounded real functions over (S subseteq mathbb {R}^{d}), i.e. (f in B(mathbb {R}^{d})) if, and only if, f has domain S and ∥f∥ ∞ <∞.

By using our result, we establish the existence of solution for the following an integral equations: x ( c ) = ϕ ( c ) + ∫ a b K ( c, r, x ( r ) ) d r, where b > a ≥ 0, x ∈ C [ a, b ] (the set of continuous real functions defined on [ a, b ] ⊆ R ), ϕ : [ a, b ] → R, and K : [ a, b ] × [ a, b ] × R → R are given mappings.

where b > a ≥ 0. The purpose of this section is to present an existence theorem for a solution to (3.1) that belongs to X = C [ a, b ] (the set of continuous real functions defined on [ a, b ] ) by using the obtained result in Corollary 2.4.