Measure theory | Real analysis | Types of functions
In the mathematical field of real analysis, a simple function is a real (or complex)-valued function over a subset of the real line, similar to a step function. Simple functions are sufficiently "nice" that using them makes mathematical reasoning, theory, and proof easier. For example, simple functions attain only a finite number of values. Some authors also require simple functions to be measurable; as used in practice, they invariably are. A basic example of a simple function is the floor function over the half-open interval [1, 9), whose only values are {1, 2, 3, 4, 5, 6, 7, 8}. A more advanced example is the Dirichlet function over the real line, which takes the value 1 if x is rational and 0 otherwise. (Thus the "simple" of "simple function" has a technical meaning somewhat at odds with common language.) All step functions are simple. Simple functions are used as a first stage in the development of theories of integration, such as the Lebesgue integral, because it is easy to define integration for a simple function and also it is straightforward to approximate more general functions by sequences of simple functions. (Wikipedia).
Pre-Calculus - Vocabulary of functions
This video describes some of the vocabulary used with functions. Specifically it covers what a function is as well as the basic idea behind its domain and range. For more videos visit http://www.mysecretmathtutor.com
From playlist Pre-Calculus - Functions
Functions of equations - IS IT A FUNCTION
👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
(New Version Available) Inverse Functions
New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/
From playlist Exponential and Logarithmic Expressions and Equations
What is a Function? Calculus for Beginners: Dr Chris Tisdell Live Stream
What is a function and how are they useful? This video will answer these questions from an elementary mathematics point of view. Functions are a bit like a machine that follows a processing rule. You input something (like a number), the machine processes the number according to the rule,
From playlist Calculus for Beginners
Determine if a Relation is a Function
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From playlist Intro to Functions
2.11117 What is a rational function Functions
http://www.freemathvideos.com presents: Learn math your way. My mission is to provide quality math education to everyone that is willing to receive it. This video is only a portion of a video course I have created as a math teacher. Please visit my website to join my mailing list, downloa
From playlist Rational Functions - Understanding
Define an inverse function. Determine if a function as an inverse function. Determine inverse functions.
From playlist Determining Inverse Functions
Using the vertical line test to determine if a graph is a function or not
👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Determine if the equation represents a function
👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=TXMCTAF6SEE&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Simple Zeros of Modular Form L-Functions - Alexandre de Faveri
Members' Colloquium Topic: Simple Zeros of Modular Form L-Functions Speaker: Alexandre de Faveri Affiliation: Member, School of Mathematics Date: April 03, 2023Â Zeros of L-functions have been extensively studied, due to their close connection to arithmetic problems. Despite several prec
From playlist Mathematics
Measure Theory - Part 6 - Lebesgue integral
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From playlist Measure Theory
Measure Theory - Part 6 - Lebesgue integral [dark version]
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From playlist Measure Theory [dark version]
Lecture 11: The Lebesgue Integral of a Nonnegative Function and Convergence Theorems
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=ZWzCHjN3_3s&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Functional Analysis Lecture 04 2014 01 30 Dual L^p spaces
Isometry between Dual L^p and L^p’; key lemma
From playlist Course 9: Basic Functional and Harmonic Analysis
A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 1)
In the first two lectures I will try to tell (or, rather, to give an idea) of how Maryam Mirzakhani has counted simple closed geodesics on hyperbolic surfaces. I plan to briefly mention her count of Weil-Peterson volumes and her proof of Witten's conjecture, but only on the leve
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
In this video, I prove the famous Riemann-Lebesgue lemma, which states that the Fourier transform of an integrable function must go to 0 as |z| goes to infinity. This is one of the results where the proof is more important than the theorem, because it's a very classical Lebesgue integral
From playlist Real Analysis
Simple zeros of L-functions - Alexandre Perozim de Faveri
Short Talks by Postdoctoral Members Topic: Simple zeros of L-functions Speaker: Alexandre Perozim de Faveri Affiliation: Member, School of Mathematics Date: September 22, 2022
From playlist Mathematics
Python Functions Tutorial | Working With Functions In Python | Python Training | Edureka
🔥 Python Certification Training: https://www.edureka.co/data-science-python-certification-course This Edureka video on Python Functions tutorial covers all the important aspects of functions in Python right from the introduction to what functions are, all the way till checking out the ma
From playlist Python Programming Tutorials | Edureka
What is a function? How do you use the vertical line test? Learn more about functions and determine if mappings, sets of ordered pairs, tables, or graphs are functions in this short algebra video. Need more math help? Check out our algebra and geometry lessons at katesmathlessons.com
From playlist Algebra 1