Measure Theory pp 103-121 | Cite as

Hilbert Space

  • J. L. Doob
Part of the Graduate Texts in Mathematics book series (GTM, volume 143)


The L p space of functions on a measure space (S, S,λ) was discussed in Section VI. 14. The special case p = 2 plays a strong role in analysis and will now be discussed in more detail in an abstract form. It is useful to allow complex valued measurable functions in this study. Complex conjugates are indicated by upper bars. Recall that a complex valued function f is measurable if and only if its real part ℜf and imaginary part ℑf are.


Hilbert Space Equivalence Class Fourier Coefficient Unitary Transformation Measure Theory 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • J. L. Doob
    • 1
  1. 1.UrbanaUSA

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