Measure, Integration & Real Analysis · Problem 11C.15

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · fourier-transform-not-L1

Problem

Define f∈L1(R)f \in L^1(\mathbf{R}) by f(x)=e−x4χ[0,∞)(x)f(x) = e^{-x^4}\chi_{[0,\infty)}(x). Show that f^∉L1(R)\hat{f} \notin L^1(\mathbf{R}).

Related theory

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