## Symmetric Properties of Real FunctionsThis work offers detailed coverage of every important aspect of symmetric structures in function of a single real variable, providing a historical perspective, proofs and useful methods for addressing problems. It provides assistance for real analysis problems involving symmetric derivatives, symmetric continuity and local symmetric structure of sets or functions. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preface | 1 |

CONTINUITY | 23 |

COVERING THEOREMS | 63 |

EVEN PROPERTIES | 111 |

MONOTONICITY | 183 |

ODD PROPERTIES | 213 |

THE SYMMETRIC DERIVATIVE | 249 |

SYMMETRIC VARIATION | 293 |

SYMMETRIC INTEGRALS | 323 |

APPENDIX | 403 |

PROBLEMS | 421 |

427 | |

441 | |

### Common terms and phrases

2-interval apply approximate symmetric derivative approximately continuous argument assertion Baire class Baire property Borel set bounded Charzyriski choose completes the proof condition converges convex Corollary countable set covering theorem defined definition Denjoy-Perron integral denote the set dense set density point elementary endpoints everywhere symmetrically exists f be measurable f is continuous F(x h finite follows Freiling function f Hamel basis inequality Khintchine Lebesgue integrable Lemma Let f Let the function limsup linear locally symmetric measurable function measurable set measure zero midpoint-linear monotonicity theorem nondecreasing function nonmeasurable obtain open set ordinary derivative outer measure point XQ points of continuity positive measure positive number prove real numbers rectangle Riemann satisfies scattered set SDf(x second symmetric derivative Section semicontinuous sequence set of points smooth functions subinterval subset Suppose that f symmetric functions symmetrically continuous function symmetrically differentiable trigonometric series write Zygmund

### References to this book

Theory of Differentiation: A Unified Theory of Differentiation Via New ... Krishna M. Garg No preview available - 1998 |