Semi- Continuity: Semi- Continuity, Mathematical Analysis, Extended Real Number - Softcover

 
9786131120749: Semi- Continuity: Semi- Continuity, Mathematical Analysis, Extended Real Number
Softcover
ISBN 10: 6131120749 ISBN 13: 9786131120749
Verlag: OmniScriptum, 2010

Inhaltsangabe

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical analysis, semi-continuity (or semicontinuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f is upper (lower) semi-continuous at a point x0 if, roughly speaking, the function values for arguments near x0 are either close to f(x0) or less than (greater than) f(x0).Consider the function f, piecewise defined by f(x) = –1 for x < 0 and f(x) = 1 for x ≥ 0. This function is upper semi-continuous at x0 = 0, but not lower semi-continuous.A function is continuous at x0 if and only if it is upper and lower semi-continuous there. Therefore, semi-continuity can be used to prove continuity. If f and g are two real-valued functions which are both upper semi-continuous at x0, then so is f + g. If both functions are non-negative, then the product function fg will also be upper semi-continuous at x0. Multiplying a positive upper semi-continuous function with a negative number turns it into a lower semi-continuous function.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical analysis, semi-continuity (or semicontinuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f is upper (lower) semi-continuous at a point x0 if, roughly speaking, the function values for arguments near x0 are either close to f(x0) or less than (greater than) f(x0).Consider the function f, piecewise defined by f(x) = –1 for x < 0 and f(x) = 1 for x ≥ 0. This function is upper semi-continuous at x0 = 0, but not lower semi-continuous.A function is continuous at x0 if and only if it is upper and lower semi-continuous there. Therefore, semi-continuity can be used to prove continuity. If f and g are two real-valued functions which are both upper semi-continuous at x0, then so is f + g. If both functions are non-negative, then the product function fg will also be upper semi-continuous at x0. Multiplying a positive upper semi-continuous function with a negative number turns it into a lower semi-continuous function.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
OmniScriptum
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
6131120749
ISBN 13 
9786131120749
Einband
Tapa blanda
Anzahl der Seiten
96
Herausgeber
Surhone Lambert M., Timpledon Miriam T., Marseken Susan F.
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar