OnL¹Space Formed by Real-Valued Partial Functions

• Autorzy: Yasushige Watase , Noboru Endou , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

This article contains some definitions and properties refering to function spaces formed by partial functions defined over a measurable space. We formalized a function space, the so-called L1 space and proved that the space turns out to be a normed space. The formalization of a real function space was given in [16]. The set of all function forms additive group. Here addition is defined by point-wise addition of two functions. However it is not true for partial functions. The set of partial functions does not form an additive group due to lack of right zeroed condition. Therefore, firstly we introduced a kind of a quasi-linear space, then, we introduced the definition of an equivalent relation of two functions which are almost everywhere equal (=a.e.), thirdly we formalized a linear space by taking the quotient of a quasi-linear space by the relation (=a.e.).MML identifier: LPSPACE1, version: 7.9.03 4.108.1028

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2008
• Tom: 16
• Numer: 4
• Strony: 361-369

Daty

wydano

2008-01-01

online

2009-03-20

Twórcy

autor

Yasushige Watase

• Shinshu University, Nagano, Japan

autor

Noboru Endou

• Gifu National College of Technology, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

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Identyfikatory

DOI

10.2478/v10037-008-0044-9