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A point on the real number line that is associated with a coordinate is called its graph. To construct a number line, draw a horizontal line with arrows on both ends to indicate that it continues without bound. Next, choose any point to represent the number zero; this point is called the origin. Figure 1.1.2.
composition of. L. p. functions. Suppose f, g ∈ L p ( R), ( 1 ≤ p < ∞). For simplicity, let us assume that, g, f: R → R so that composition of f and g, namely, f ∘ g ( x) = f ( g ( x)); ( x ∈ R) is well-defined. My Question is: Given real-valued functions f, g ∈ L p ( R).
In musicology, the opus number is the "work number" that is assigned to a musical composition, or to a set of compositions, to indicate the chronological order of the composer's production. Opus numbers are used to distinguish among compositions with similar titles; the word is abbreviated as "Op." for a single work, or "Opp." when referring to
1 Answer. If fact for every p p and q q there is a function f f with ∥f∥p < ∞ ‖ f ‖ p < ∞ and ∥f∥q = ∞ ‖ f ‖ q = ∞. Using this you can show that for any measure space X X (I'm assume your questions is about Lp(R) L p ( R)) if there is a p p and q q with ∥ ⋅∥p ‖ ⋅ ‖ p equivalent to ∥ ⋅∥q ‖ ⋅ ‖ q .
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