Chapter2
Next, we consider the supremum and infimum of linear combinations of func-tions. Scalar multiplication by a positive constant multiplies the inf or sup, while multiplication by a negative constant switches the inf and sup, Proposition 2.15. Suppose that f : A → Ris a bounded function and c ∈ R. If c ≥ 0, then sup A cf = csup A f, inf A ...
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