Hilbert Spaces: Lebesgue integral introduced, step functions, 2-8-23 part 1

preview_player
Показать описание

  1. James Cook Math
Рекомендации по теме
Hilbert Spaces: Lebesgue 0:59:51

Hilbert Spaces: Lebesgue integral introduced, step functions, 2-8-23 part 1

Hilbert Spaces: Lebesgue 0:59:11

Hilbert Spaces: Lebesgue integral on RN, brief introduction to convolution, 2-24-23 part 1

Hilbert Spaces: Lebesgue 0:05:02

Hilbert Spaces: Lebesgue integral introduced, step functions, 2-8-23 part 2

Hilbert Spaces: Lebesgue 0:11:06

Hilbert Spaces: Lebesgue integral on RN, brief introduction to convolution, 2-24-23 part 2

Lecture 12: Lebesgue 1:24:57

Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence...

Measure Theory, Functional 0:15:46

Measure Theory, Functional Analysis, and The Lebesgue Integral for Undergraduates - Johnston

Real and Functional 0:00:28

Real and Functional Analysis

An Introductory Course 0:01:21

An Introductory Course in Lebesgue Spaces

Hilbert Spaces: Riemann 0:59:50

Hilbert Spaces: Riemann Integral vs. Lebesgue, word on measurable sets, 2-22-23

Hilbert Spaces: Lebesgue 0:33:26

Hilbert Spaces: Lebesgue integrable function theory, Section 2.3 in book, 2-10-23 part 1

Why greatest Mathematicians 0:00:38

Why greatest Mathematicians are not trying to prove Riemann Hypothesis? || #short #terencetao #maths

Measure Theory & 0:40:14

Measure Theory & Functional Analysis 8: Riemann Integral vs Lebesgue Integral

How REAL Men 0:00:35

How REAL Men Integrate Functions

Lebesgue integral for 0:25:43

Lebesgue integral for complex and real measurable functions: the space of L^1 functions

Lebesgue Integration on 0:50:45

Lebesgue Integration on Euclidean Space Jones and Bartlett books in mathematics Frank Jones

Lecture 13: Lp 1:23:59

Lecture 13: Lp Space Theory

Kolmogorov, Fomin 0:13:10

Kolmogorov, Fomin Measure, Lebesgue Integral And Hilbert Space Academic Press 1961

Inner Products in 0:08:41

Inner Products in Hilbert Space

Lebesgue Integration -- 0:08:13

Lebesgue Integration -- simple problems

Hilbert Spaces: Lebesgue 0:20:10

Hilbert Spaces: Lebesgue integrable function theory, Section 2.3 in book, 2-10-23 part 2

Hilbert Spaces: locally 0:59:51

Hilbert Spaces: locally integrable functions, 2-20-23 part 1

With Hilbert Space 0:10:05

With Hilbert Space Miller, lebesgue

Lecture 5 Lp 0:50:59

Lecture 5 Lp Spaces on the real line

Measure, Lebesgue Integrals, 0:13:10

Measure, Lebesgue Integrals, and Hilbert Space Academic Press, New Y A N Fomin, S V Kolmogorov

Комментарии
Автор

The integral of step functions is well-defined do to the fact that it does not depend the representation of the step function. I feel a bit embarrasing asking this, but I have trouble approaching its proof. Could you provide some hint?

I guess a proof can start like this: let f be a step function and
p_1f_1+...+ p_nf_n,
q_1g1+...+q_mg_m
both be representations of $f$, where f_k, g_l are characteristic functions of [a_k, b_k), [a'_l, b'_l) respectively.
Need to show: p_1(b_1-a_1) + ... + p_n(b_n-a_n) = q_1(b'_1-a'_1) + ... + q_m(b'_l - a'_l)

Then I'm not sure how to proceed...

mingmiao