Locally finite measure

In linear algebra, functional analysis and related areas of mathematics, a quasinorm is similar to a norm in that it satisfies the norm axioms, except that the triangle inequality is replaced by

$\Vert x+y\Vert \le K(\Vert x\Vert +\Vert y\Vert )$

for some $K>1.$

This is not to be confused with a seminorm or pseudonorm, where the norm axioms are satisfied except for positive definiteness.

Related concepts

A vector space with an associated quasinorm is called a quasinormed vector space.

A complete quasinormed vector space is called a quasi-Banach space.

A quasinormed space $(A,\Vert \cdot \Vert )$ is called a quasinormed algebra if the vector space A is an algebra and there is a constant K > 0 such that

$\Vert xy\Vert \le K\Vert x\Vert \cdot \Vert y\Vert$

for all $x,y\in A$.

A complete quasinormed algebra is called a quasi-Banach algebra.

See also

• Seminorm

References

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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534