In mathematics, with special application to complex analysis, a normal family is a pre-compact subset of the space of continuous functions. Informally, this means that the functions in the family are not widely spread out, but rather stick together in a somewhat "clustered" manner. Note that a compact family of continuous functions is automatically a normal family.
Sometimes, if each function in a normal family F satisfies a particular property (e.g. is holomorphic),
then the property also holds for each limit point of the set F.
More formally, let X and Y be topological spaces. The set of continuous functions has a natural topology called the compact-open topology. A normal family is a pre-compact subset with respect to this topology.
If Y is a metric space, then the compact-open topology is equivalent to the topology of compact convergence,[1] and we obtain a definition which is closer to the classical one: A collection F of continuous functions is called a normal family
if every sequence of functions in F contains a subsequence which converges uniformly on compact subsets of X to a continuous function from X to Y. That is, for every sequence of functions in F, there is a subsequence and a continuous function from X to Y such that the following holds for every compact subset K contained in X:
A NormalFamily (Korean: 보통의 가족) is a 2023 South Korean drama film directed by Hur Jin-ho, and starring Sol Kyung-gu, Jang Dong-gun, Kim Hee-ae, and Claudia...
analysis, a normalfamily is a pre-compact subset of the space of continuous functions. Informally, this means that the functions in the family are not widely...
A Nearly NormalFamily (sv: En helt vanlig familj) is a 2023 Swedish drama limited television series directed by Per Hanefjord, and developed by Hans...
Normal(s) or The Normal(s) may refer to: Look up normal in Wiktionary, the free dictionary. Normal (2003 film), starring Jessica Lange and Tom Wilkinson...
In probability theory, the family of complex normal distributions, denoted C N {\displaystyle {\mathcal {CN}}} or N C {\displaystyle {\mathcal {N}}_{\mathcal...
A Perfectly NormalFamily (Danish: En helt almindelig familie) is a 2020 Danish drama film directed by Malou Reymann and starring Mikkel Boe Følsgaard...
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued...
The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions...
and family: A NormalFamily, A Normal Life, A Normal Love, A Normal Imagination, A Normal Nature, A Normal Universe, A Normal Communication, A Normal Ageing...
theory rather than potential theory. His proof used Montel's concept of normalfamilies, which became the standard method of proof in textbooks. Carathéodory...
and The New Normal, and is also known for her work on Chuck and Family Guy. Adler was born in Montreal, Quebec, Canada, to a Jewish family. Her grandfather...
Menagerie. He has also directed an original play in Kochi called A Very NormalFamily with a new team of artists based in the city. Roshan made his screen...
units were sold, providing homes for 84,000 people. In addition to normalfamily dwellings, Levittowns provided private meeting areas, swimming pools...
Normal People is a 2018 novel by the Irish author Sally Rooney. Normal People is Rooney's second novel, published after Conversations with Friends (2017)...
is a list of episodes for the American television sitcom The Partridge Family. All four seasons have been released on DVD by Sony Pictures. "Special Collector's...
premiered May 2024. She is one of the main lead in the film. 2019: A Very NormalFamily (Mollyamma) Kerala State Television Awards 2015: Kerala State Television...
what happened in Libya and that "the Gaddafi family is not how they are being depicted, they are normal people". Hessler is Catholic but considers herself...
find out who might have wanted to kill an apparently normal girl from an apparently normalfamily. A possible clue comes at the funeral, when Patricia's...
normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution...
challenges each of them face during the constant pursuit of maintaining a normalfamily dynamic. He has one son. "Harney's IMDB pro page" Entertainment industry...
incarcerating Jack will not bring her family back. When Jack is released, he is unable to reincorporate himself into normalfamily life, and instead leaves home...
Next to Normal is a 2008 American rock musical with book and lyrics by Brian Yorkey and music by Tom Kitt. The story centers on a mother who struggles...
Cambridge. Day has stated that she came from "a very normalfamily with very normal jobs" as none of her family had ties to the entertainment industry. When five...
Global Information
