## Mathematical foundations of quantum mechanics: lectures delivered at the University of Virginia, 1946-47 |

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### Contents

Relations and Functions | 3 |

Metric Spaces | 8 |

InnerProduct Spaces | 20 |

17 other sections not shown

### Common terms and phrases

belong Cauchy sequence characteristic function characteristic numbers characteristic vectors choose classical mechanics complex numbers continuous functions convergent series converges coordinate frame corresponds countable set definition denote dense distribution function domain elementary measure elementary set exists f and g f(x)mdx finite number force function f Hence Hermitian operator hich holds identity inequality inner-product space integrable with respect integral of f interval L-function left member Let f limit linear combination linear functions measure function metric space motion non-negative notation ordered pairs orthogonal orthogonal complement orthonormal set particles partition polynomial positive integers positive number projection operator properties prove range real number real-valued right member RS-integrable satisfied self-adjoint self-adjoint operators step-function subset summable Suppose tends theorem tion U-functions U(tQ uniformly continuous variable vectors f x)mdx zero