Every continuous function is measurable||inverse image is measurable LEC 10(measure Theory)

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In this Lecture, Students will be able to understand the concept of measurable functions and the following theorems.
1. Let f be any real-valued function defined on a measurable domain D and G an Open set in R. Then f is measurable if and only if f^(-1) (G) is measurable.
2. Every continuous function is measurable.
3. the map of mathematics

@measuretheory1598 @MEASURE THOU THE TIME DILIGENTLY
@brightsideofmaths @mathforall6404 @STANDARDSTUDY @Fematika
#measuretheory #mathematics #measure #maths #continuous #inversefunctions #gate #discrete
  1. The Map of Mathematics
  2. measure
  3. measure theory
  4. measurable functions
  5. continuous function is measurable
  6. continues function
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Комментарии
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Thanks for uploading an informative lecture.

salmanshah-uyxc
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Thanks a lot sir je well present MashAllah

aamirhaneef
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Hlo sir ek therom krwa do
Every measurable function is continuous prove or disprove

PreetgognaGogna
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Seriously prof. No doubts after see this lec… itx very helpful for uss
aWaiting yr nxt lec…
Thnk u

madihariaz
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You have error
Every inverse image of open interval is not going to open interval.
Because we thinking about every possible function its possible we get some open set instead of open interval as image of open interval.

And every open set of R is not measurable (EX let A be some open sub set of R and intersection of open set and vitali set is open for atleast some case then this open set is not measurable)

Correction,
inverse image of open set is open and every open set is borel set which measurable so our set
{x : f(x)> alfa } for every alfa belong to R
Is measurable.

NDjayswal