### Abstract

Lp is the space of functions whose p-th power is integrable. It is one of the most fundamental Banach spaces that is used in analysis and probability. We develop a framework for function spaces, and then implement the Lp spaces in this framework using the existing integration theory in Isabelle/HOL. Our development contains most fundamental properties of Lp spaces, notably the Hölder and Minkowski inequalities, completeness of Lp, duality, stability under almost sure convergence, multiplication of functions in Lp and Lq, stability under conditional expectation.

### License

BSD License

### Topics

- Mathematics/Analysis

### Session Lp

- Functional_Spaces
- Lp

### Depends on

- Ergodic Theory

### Used by

- Concentration Inequalities
- Formalization of Randomized Approximation Algorithms for Frequency Moments
- Fourier Series

## Cite

×

Lp-AFP

    @article{Lp-AFP,
      author  = {Sebastien Gouezel},
      title   = {Lp spaces},
      journal = {Archive of Formal Proofs},
      month   = {October},
      year    = {2016},
      note    = {\url{https://isa-afp.org/entries/Lp.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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Older releases:

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