Measure Theory · Calculus
Lᵖ Spaces and Completeness
Lᵖ spaces are complete normed vector spaces. L² is a Hilbert space; Fourier series are orthonormal expansions in L², and Parseval’s theorem is Pythagoras in infinite dimensions.
WHAT STUDENTS WILL LEARN
✓Define Lᵖ spaces via the p-norm
✓Prove completeness (Riesz-Fischer)
✓Apply Hölder’s and Minkowski’s inequalities
✓Understand L² as a Hilbert space
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