lower semicontinuous function - significado y definición. Qué es lower semicontinuous function
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Qué (quién) es lower semicontinuous function - definición

PROPERTY OF FUNCTIONS WEAKER THAN CONTINUITY
Semicontinuous; Semicontinuity; Semi-continuous; Lower semi-continuous; Upper semi-continuous; Lower semicontinuous; Upper semicontinuous; Semi-continuous function; Semi-continuous mapping; Semicontinuous function; Upper-semicontinuous; Upper semicontinuity; Lower semicontinuity; Upper semi-continuity; Lower semi-continuity
  • A lower semicontinuous function that is not upper semicontinuous. The solid blue dot indicates <math>f\left(x_0\right).</math>
  • An upper semicontinuous function that is not lower semicontinuous. The solid blue dot indicates <math>f\left(x_0\right).</math>

Semi-continuity         
In mathematical analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f is upper (respectively, lower) semicontinuous at a point x_0 if, roughly speaking, the function values for arguments near x_0 are not much higher (respectively, lower) than f\left(x_0\right).
Function (mathematics)         
  • A binary operation is a typical example of a bivariate function which assigns to each pair <math>(x, y)</math> the result <math>x\circ y</math>.
  • A function that associates any of the four colored shapes to its color.
  • Together, the two square roots of all nonnegative real numbers form a single smooth curve.
  • Graph of a linear function
  • The function mapping each year to its US motor vehicle death count, shown as a [[line chart]]
  • The same function, shown as a bar chart
  • Graph of a polynomial function, here a quadratic function.
  • Graph of two trigonometric functions: [[sine]] and [[cosine]].
  • right
ASSOCIATION OF A SINGLE OUTPUT TO EACH INPUT
Mathematical Function; Mathematical function; Function specification (mathematics); Mathematical functions; Empty function; Function (math); Ambiguous function; Function (set theory); Function (Mathematics); Functions (mathematics); Domain and range; Functional relationship; G(x); H(x); Function notation; Output (mathematics); Ƒ(x); Overriding (mathematics); Overriding union; F of x; Function of x; Bivariate function; Functional notation; Function of several variables; Y=f(x); ⁡; Draft:The Repeating Fractional Function; Image (set theory); Mutivariate function; Draft:Specifying a function; Function (maths); Functions (math); Functions (maths); F(x); Empty map; Function evaluation
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously.
Lower Arrernte language         
EXTINCT AUSTRALIAN ABORIGINAL LANGUAGE
Lower Aranda language; Lower Arrernte dialect; Lower Arrernte; Lower Southern Aranda language; Lower Aranda; ISO 639:axl; Lower Aranda dialect; Lower Southern Aranda; Alenjerntarpe language; Alenjerntarrpe
Lower Arrernte, also known as Lower Southern Arrernte, Lower Aranda, Lower Southern Aranda and Alenjerntarrpe, was an Arandic language (but not of the Arrernte language group). Lower Arrernte was spoken in the Finke River area, near the Overland Telegraph Line station at Charlotte Waters, just north of the border between South Australia and the Northern Territory, and in the Dalhousie area in S.

Wikipedia

Semi-continuity

In mathematical analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f {\displaystyle f} is upper (respectively, lower) semicontinuous at a point x 0 {\displaystyle x_{0}} if, roughly speaking, the function values for arguments near x 0 {\displaystyle x_{0}} are not much higher (respectively, lower) than f ( x 0 ) . {\displaystyle f\left(x_{0}\right).}

A function is continuous if and only if it is both upper and lower semicontinuous. If we take a continuous function and increase its value at a certain point x 0 {\displaystyle x_{0}} to f ( x 0 ) + c {\displaystyle f\left(x_{0}\right)+c} for some c > 0 {\displaystyle c>0} , then the result is upper semicontinuous; if we decrease its value to f ( x 0 ) c {\displaystyle f\left(x_{0}\right)-c} then the result is lower semicontinuous.

The notion of upper and lower semicontinuous function was first introduced and studied by René Baire in his thesis in 1899.